There are two tasks for the Body of Christ, in order to be salt and light in our world:
Task #1: How should Christians guide the human race in preventing murders?
Task #2: How should Christians guide the human race in dealing with murderers if we fail Task #1?
"The State" is usually the answer to #2: Execute murderers.
But "The State" is also involved in Task #1: First, virtually every State today prohibits State-run school teachers from teaching students that God in the Bible prohibits murder. Murder is never said to offed the God of the Bible, but only the State.
Second, "the State" commits more murders than "private sector" murderers by orders of magnitude. R.J. Rummel has written about "democide," government murder of "its own people." His higher estimates of internal government murder is a quarter of a billion people in the 20th century. Then there is war, government murder of the people of some other government. Higher estimates for WWII are 90 million. Total estimates for murder by war in the 20th century are again about a quarter of a billion people. That's over 10,000 murders PER DAY by the State, as compared with a similar number of private-sector murders in the U.S. PER YEAR.
And yet when I propose that the human race should agree that "Thou shalt not kill" should apply to everyone, even to the State, I'm told that (1) I'm "some kind of anarchist" (a person of bad moral character), and (2) "murderers will take over the world" if my utopian views are adopted.
It seems to me that murderers have ALREADY taken over the world, and their Trojan Horse was this institution called "The State." 10,000 murders a day. How could it be worse under principled Theonomic Christian-directed anarchy?
"The State" also legalizes the murder of the unborn, to the tune of 130,000 PER DAY worldwide.
I think Christians in the U.S. have the financial and media power to abolish all governments in the world. But that's another subject.
OK then, what do we do with murderers after we abolish the State (because we will have them, even in my utopian "Vine & Fig Tree" world)? More specifically, "What does God want us to do with a murderer?"
Does God want us to shed the murderer's blood to make atonement (Numbers 35:33)?
I reject secular vengeance as a Biblical response.
So I have to admit I don't see a clear Biblical mandate for dealing with a murderer if we fail to prevent a murder. I tend to favor a form of lifetime restitution to the estate of the victim. In other words, the murderer is required to work for the victim's heirs for the rest of his life. This can be required but not compelled, as I suggest here (audio).