As to the Constitutionality of capital punishment, read the first clause of the Fifth Amendment.
As to the state government committing murder in the performance of an execution of sentence, the state governments are sovereign governments, like it or not, they have dominion.
Here in Kansas City (Independence actually) a few days ago we had a case in which a young man just released from jail stole a Chevy Blazer. There was a six year-old boy in the back seat. The thief threw the boy out of the door, but he was entangled in the seat belt. The boy was dragged over five miles at speeds of up to eighty miles an hour before he was stopped and subdued by private citizens. The boy was, of course, dead by then.
How much concern should we have for this man's well being? Should we lock him up again (he already has a couple of felony convictions)? Why not just give him a fair trial, find him guilty of capital murder, and execute him?
One of those things I wish I’d said. The best response to this question I’ve ever seen when asked to explain why some endorse the former and not the latter. Quicksilver, a Lycos message board poster responded that he wished to punish the perpetrator of the one act, but desired to protect the victim of the other.