Why couldn't the Cheshire Cat be beheaded?

The Cheshire Cat does have a body. It also has the ability to vanish and reappear. Not only that, but it can vanish whichever parts of its body it chooses. So, in the book, when Alice meets it in the forest, it disappears very slowly, starting at the tail and eventually leaving just its grin behind. And when it appears at the Queen's croquet game, it only reveals its head, creating the impression that it has no body.