Long before God gave the law of Moses, he made it universal law for man after the flood that man must execute whoever sheds the blood of man (Genesis 9: 6). History says that nearly everybody in the past treated executing criminals as something that had some kind of supernatural mandate and origin. It to their heads was obviously just and sensible. Paul writes about a commonsense law of God that people have when they don’t have the Law of Moses and that people had before it. He was elevating capital punishment to reason. Paul used this reasoning to work out how you can have no Law of Moses and still be a sinner. Part of the reason for executing murderers is that they killed the image of God. To show hate for a man and kill him is to intend to do it for the creator too. Opposition to capital punishment is really a secular humanistic venture.  By implication the secular approach accuses religion of murder or of opening the door to it.

Jesus took the death penalty for sins so the Bible says. To emphasise that in some way Jesus rewarded the thief on the cross with eternal life who said he deserved to be on the cross for his crimes. See Luke 23:41-43 New International Version (NIV).

41 We are punished justly, for we are getting what our deeds deserve. But this man has done nothing wrong.”

42 Then he said, “Jesus, remember me when you come into your kingdom.”

43 Jesus answered him, “Truly I tell you, today you will be with me in paradise.”

Jesus said that the Old Testament was infallible and was God's revelation and his unbreakable word. If Jesus was God, then he made the vicious laws of God given in the Bible that demanded that heretics and homosexuals and whole nations be violently slain by his people.

The God of the Bible only commands executing people who do what is considered immoral.  There is no death penalty for those who break cultural religious rules such as not celebrating Passover.  So the death penalty communicates that homosexuality, bestiality, adultery, idolatry, being a fake prophet of God, spiritist and many other deeds are horrendously immoral and intolerable.  The idea is that these sins are so bad that they make it necessary to destroy the sinner.  This is a side-effect of condemning the sin.

Capital punishment is seen as an act of just and unavoidable war by a state against its own citizens who need destruction for being so dangerous and for killing others.  That is the belief of the Church even though it may now say that there is too much injustice to risk allowing capital punishment for it will be abused.  The principle is still maintained.   The Churches then as long as they approve the just war doctrine have to be open to agreeing with capital punishment and supporting those who implement it.

In his book Where Does it say that in the Bible? page 164 on the inquisition Catholic scholar Patrick Madrid quotes with approval the text of Deuteronomy 17:2 to 7 where scripture commands that a man or woman who adores gods other than God are to be stoned to death. It commands that the witnesses must be the first to lift the stones.  By approval he means that if it were reinstated today by God it should be obeyed.

Madrid could have pointed to 2 Chronicles 15.  This scripture approves of Asa murdering women and children as well as men who wanted other gods beside God. 

"10  They assembled at Jerusalem in the third month of the fifteenth year of Asa’s reign. 11 At that time they sacrificed to the Lord seven hundred head of cattle and seven thousand sheep and goats from the plunder they had brought back. 12 They entered into a covenant to seek the Lord, the God of their ancestors, with all their heart and soul. 13 All who would not seek the Lord, the God of Israel, were to be put to death, whether small or great, man or woman. 14 They took an oath to the Lord with loud acclamation, with shouting and with trumpets and horns. 15 All Judah rejoiced about the oath because they had sworn it wholeheartedly. They sought God eagerly, and he was found by them. So the Lord gave them rest on every side.  16 King Asa also deposed his grandmother Maakah from her position as queen mother, because she had made a repulsive image for the worship of Asherah. Asa cut it down, broke it up and burned it in the Kidron Valley. 17 Although he did not remove the high places from Israel, Asa’s heart was fully committed to the Lord all his life. 18 He brought into the temple of God the silver and gold and the articles that he and his father had dedicated."

Matthew 5:21 has Jesus referring to the teaching of God that murder is forbidden and that whoever murders must be subjected to judgment. By judgment he means capital punishment. Jesus goes on to say the Sanhedrin should have the right to administer such physical punishment to those who call their brother a fool. The Sanhedrin is declared then to have the right to do what it does which implies support for its claim that it has the divine right to decree executions by stoning.

The Church says that Jesus saved the life of an adulteress in John 6. Some use this story to argue that Jesus did away with the capital punishment laws. There a woman was caught in adultery and hauled before Jesus by a mob who asked Jesus if they should stone her to death. He said that if anybody was without sin let him be the first to cast a stone at her. This certainly says that a sinless accuser could indeed stone her to death. They all walked away and Jesus told the woman to go and sin no more. Some say that he could have stoned her being sinless and he didn't so he didn't agree with stoning women like her though the law commanded stoning for such. But the woman had been hauled before him by a mob not the legal system. Had these people been really concerned for the law they would have had a warrant to stone her. They didn't when they were able to walk away. The story does not teach that capital punishment is wrong. Quite the opposite. It implies that adulterous people should be destroyed but through the proper channels and by fair courts. Jesus and the early Church did not believe that magistrates had to be sinless before they had the right to punish offenders. They punish as representatives of the law not in their personal capacity. They are doing a job.
The Church agrees with the evil laws made by God in the Old Testament. Jesus Christ in John 8:7,11 said that the only objection he had to the woman being stoned to death of adultery was that the accusers were no better themselves. If they had been sinless he would have agreed. Read page 16 of Apologia Catholic Answers to Today’s Questions. The Church would say that if we could go back in time far enough, we would have to keep those laws. This makes the Church a murderer in its heart (Matthew 5).  Jews when able to, put adulterous people to death. What about Jesus telling the Jews to judge men or women who remarried after divorce as guilty of adultery?   He said that to Jewish leaders who were also lawyers meaning he was virtually telling them to execute the divorced and remarried and not just cheaters.

Jesus told the Jews off for not executing young men who cursed their parents and said they annulled the commandment of God in doing so.
Indeed Jesus supposedly saved the soul of the thief who was crucified with him because the thief confessed that he deserved the cross. Jesus told him that he would be saved that very day implying that the thief was a saint just for approving of what the evil Romans did to him.

The Bible gives no hint that the laws of God commanding the killing of murderers, homosexuals and adulterers etc in the Old Testament were temporary civil laws. It does not say they were only state laws. If they are moral laws then they are still valid for today's Christians.

Read what Peter, Jesus' apostle said in the Acts of the Apostles. The context is how Jesus was supposedly murdered as a result of Jewish scheming. "Now, fellow Israelites, I know that you acted in ignorance, as did your leaders. But this is how God fulfilled what he had foretold through all the prophets, saying that his Messiah would suffer. Repent, then, and turn to God, so that your sins may be wiped out, that times of refreshing may come from the Lord, and that he may send the Messiah, who has been appointed for you—even Jesus. Heaven must receive him until the time comes for God to restore everything, as he promised long ago through his holy prophets. For Moses said, ‘The Lord your God will raise up for you a prophet like me from among your own people; you must listen to everything he tells you. Anyone who does not listen to him will be completely cut off from their people.’" Peter adds the command about being cut off to that text. In the Law, it does not appear beside that command but it does appear in relation to other subjects such as sabbath breakers. Cutting off appears in the Law of Moses which apparently refers to somebody being thrown out of the community and left to die in the wilderness. Most authorities regard it as referring to direct execution. Exodus 31 is clear that “cut off” means execute - to take the life.  Peter refers to a complete cut off which is clearly a euphemism for murdering them. Peter is endorsing Moses as commanding that those who turn to Jesus and then away from him must be executed. The method would have usually being stoning. Jesus referred to that verse about the prophet too. Peter by saying Moses and Jesus are both to be obeyed totally is indicating that both want rebel Christians put to death. He does not say it can be done but that it must be aimed for and done when possible. No sect ever claims it can just go out and execute as if the government was not there.
Jesus said that we are commanded to love God with all our hearts - so we should be willing to embrace everlasting torment if God asked us to. Such a severe message makes capital punishment seem such a little thing! We should not be surprised if God asks us to implement it! It is no reply to say that loving God just means keeping his commandments. That would be loving his commandments but we are asked to love God.