Heavy object to the head, as hard as possible. This is even more brutal than beheading, but it kills instantly and completely. No pain. I would go out on a limb and say it's less painful than euthanasia via injection, as there is no needle jab.
It's terribly unpleasant for the human, but that's hardly the point, is it? Euthanasia isn't to spare US pain. It's to spare THEM pain.