Should hopelessly insane murderers be put to death?

Imagine a totally psychotic and extremely mentally disturbed person who has a propensity to violently kill innocent people. I am talking about a really stark raving bonkers individual. This person has no capability to think and act rationally. How can this person have any rights whatsoever? Why should it be the job of the state to provide for this person when they are locked up in an asylum? Would it be moral and practical to simply execute this person, thus removing the burden of having to keep an eye on him in case he escapes and kill someone?