Nope, it's savagery...old-timey mob justice, except now everyone wears nice suits and there are chemicals and electricity instead of boiling a guy in oil.
Also I've never understood the deterrent argument. Just look at the cruel and deadly punishments devised throughout human history. Somehow people kept right on burying the hatchet in people's foreheads.
Also there are the politics of who gets a death sentence and who doesn't, and oh yeah, the prospect of the state killing an innocent person, which makes us all murderers.