It is not a matter of putting one to death for their sins, it's matter of putting one to death for breaking the law. We, as mere humans, cannot forgive sin. (We can forgive people who sin against us, but that's a completely different topic.)
If the law provides for capital punishment, and the convicted murderer chose to commit that heinous crime, he/she knew the consequence of their action. Yet, he/she chose to commit that murder and therefore chose to be executed.
Have you committed adultery, worked on the Sabbath, stole something, idolized something, and so on ???
God's law given through Moses in the written ordinances carried curses that you should be put to death for breaking those laws.
Galatians 3:13 says by Christ we have been redeemed from having to face those curses.
In
John 8:1-11 they brought this woman to Christ to see if He would go against the law, but Jesus instead of going against the law told them "he who is without sin cast the first stone."
By the law one caught in adultery was to be stoned to death, but Jesus showed that no person had the right to make this call on her life because all are guilty of sin !!!
If you believe in the death penalty you are still casting stones at one for their crime(sin) when you are guilty as well !!!
That is called being a hypocrite..........Sorry but that is what Jesus said and showed !!!
Also Jesus said "NO" to the ordinance of an eye for an eye, tooth for a tooth, etc.........In other words we are not to repay the person back in the same manner in which they did any more !!!