I would guess the main reason is that it would be too gruesome for anyone watching the execution. Also, decapitation seems almost like desecrating the condemned person's corpse, which might be considered a cruel and unusual punishment even for someone considered to be deserving of the death penalty.
I think some religions object to dismemberment.
Yes and some religions object to the death penalty?
And some religions advocate stoning to death. That doesn't make either position correct. Religion should be left out of these kinds of discussions, among many others, but sadly isn't. Let's not do anything at all, that way we'll offend less people.