State execution is essentially a simple statement that there is no evil or moral truth, since in the act of permitting itself this absolute action, it states that there is no absolute truth which can be violated. The reason state murder is employed is generally punishment for the absolute evil of murder, which naturally contradicts its own self. A state that employs the death penalty is either amoral in the sense of the implied non-existence of a moral universe, or immoral in the sense of being in direct violation of the existence of a moral universe.
It can so be seen as a statement that the state's purpose is to uphold control or impose social order, but not that this reflects any moral truth. The state tells the transgressing individual, I do as you do, but I have the greater power. And perhaps that is the greatest meaning behind the death penalty; it is the opportunity of the state to manifest to all its absolute authority and power. A hint of the nature of the beast.
It is an application of Dostoevsky's heroes pondering that in the absence of God there is no moral order, and all is permitted the individual. The state is king of the antheap, and there is no power beyond the state to punish it for its actions. "In the absence of God, I am God." So says Nietzsche's "coldest of cold monsters," the state.
Considering the desire for retribution in kind and the character upon whom death is to be inflicted as justification for execution is the clouding of the mind, the temptation towards evil by impure reasoning. As an ethical extension of such thinking, imagine a penal system of raping convicted rapists, evolving presumably from initially paid servants of the state doing the raping, but in time this possibly becoming done by technological means. The wonderful world of depraved moral nihilism.