In the Old Testament the Mosaic Law specifies no less than thirty-six capital offenses calling for execution by stoning, burning, decapitation, or strangulation. Included in the list are idolatry, magic, blasphemy, violation of the sabbath, murder, adultery, bestiality, pederasty, and incest. The death penalty was considered especially fitting as a punishment for murder since in his covenant with Noah God had laid down the principle, “Whoever sheds the blood of man, by man shall his blood be shed, for God made man in His own image” (Genesis 9:6). In many cases God is portrayed as deservedly punishing culprits with death, as happened to Korah, Dathan, and Abiram (Numbers 16). In other cases individuals such as Daniel and Mordecai are God’s agents in bringing a just death upon guilty persons.
In the New Testament the right of the State to put criminals to death seems to be taken for granted. Jesus himself refrains from using violence. He rebukes his disciples for wishing to call down fire from heaven to punish the Samaritans for their lack of hospitality (Luke 9:55). Later he admonishes Peter to put his sword in the scabbard rather than resist arrest (Matthew 26:52). At no point, however, does Jesus deny that the State has authority to exact capital punishment. In his debates with the Pharisees, Jesus cites with approval the apparently harsh commandment, “He who speaks evil of father or mother, let him surely die” (Matthew 15:4; Mark 7:10, referring to Exodus 2l:17; cf. Leviticus 20:9). When Pilate calls attention to his authority to crucify him, Jesus points out that Pilate’s power comes to him from above-that is to say, from God (John 19:11). Jesus commends the good thief on the cross next to him, who has admitted that he and his fellow thief are receiving the due reward of their deeds (Luke 23:41).
The early Christians evidently had nothing against the death penalty. They approve of the divine punishment meted out to Ananias and Sapphira when they are rebuked by Peter for their fraudulent action (Acts 5:1-11). The Letter to the Hebrews makes an argument from the fact that “a man who has violated the law of Moses dies without mercy at the testimony of two or three witnesses” (10:28). Paul repeatedly refers to the connection between sin and death. He writes to the Romans, with an apparent reference to the death penalty, that the magistrate who holds authority “does not bear the sword in vain; for he is the servant of God to execute His wrath on the wrongdoer” (Romans 13:4). No passage in the New Testament disapproves of the death penalty.
Avery Cardinal Dulles, “Catholicism & Capital Punishment” (2001)