One of the problems with the English invasions of Ireland in the 16th and 17th centuries was the difference in philosophy on how society should approach murder.
(I'm writing about this at the moment, part of a book I'm working on, so it's at the forefront of my mind.)
In Ireland, the Brehon Laws, like the Scandinavian law of the time, required that an 'Eiric' be paid by the extended family of the murderer to the family of the victim.
This was a pretty good method of stopping a) murder and b) vengeance, because it spread the responsibility out, and caused the family to put pressure on their errant member.
In England, then suffering the religious mania of the Reformation, the attitude was that a murder was an offence against God, and under the biblical injunction "An eye for an eye, a tooth for a tooth", it should be "a life for a life", and the murderer should himself or herself be killed.
It seems strange to me that the religious idea is still current 600 years later.
State execution is not an effective way of stopping murders, and seems an odd method to use; it's a bad example. If the state's a murderer, how does that make murder wrong.
If Utah wanted to end murder, the best way would be to study what states (by which I mean countries, of course) have the least murder, and what they have in common.
Of course, we're not even getting into the question of countries like China and Indonesia which execute people for things like smuggling and fraud.