Can you get tonsil stones without having tonsils?

Not typically: Tonsil stones form when mucus and food debris get stuck in crypts of tonsils, typically shouldn't occur if tonsils completely removed.

Tonsil stones: No. Tonsils form in the crypts of the tonsils. No crypts, no tonsil stones. You can, however, get food stuck in scar tissue from tonsillectomy, which can lead to debris like a tonsil stone.