The Cheshire Cat's famous ability is to disappear gradually, leaving only its grin behind. This is a key element of its personality and its presence in the story.
The moment you're likely thinking of is when Alice encounters the Cheshire Cat, and, feeling frustrated by its riddles and whimsical nature, she contemplates cutting off its head. But she doesn't actually do it!
The Cheshire Cat vanishes before Alice can act, leaving behind only its grin, which fades away slowly, as if to say, "You can't get rid of me that easily!"
The Cheshire Cat's ability to vanish and reappear is a central part of its character and its role in Alice's journey. It represents the surreal and nonsensical nature of Wonderland.