Miss Tuffsy was the previous sea snail owned by Granny before she takes in Gary. It is implied that Miss Tuffsy died due to Granny overfeeding her to fatten her up to be eaten.
Miss Tuffsy herself has never been seen in the show. However, it is possible that one of the snails in the picture on Grandma's wall could be Miss Tuffsy.
Role in episode
She is only mentioned in the episode "Have You Seen This Snail?" where Grandma mistakes Gary for Miss Tuffsy and treats him like if it he were her: they go shopping, go to a beauty salon, listen to music, and watch movies. After Gary realizes her plan, he escapes her house and goes back to SpongeBob. Grandma follows him and then picks up one of the Alley Snails that Gary met in the alleyway, thinking again they are Miss Tuffsy.