The Graveyard Shift / Krusty Love - S3-E13
Squidward: Years ago, at this very restaurant, the hatch-slinging slasher used to be a frycook, just like you. Only clumsier! And then, one night, when he was cutting the patties, it happened...
SpongeBob: He forgot the secret sauce?
Squidward: No.
SpongeBob: He didn't wash his hands?
Squidward: No!
SpongeBob: Irregular portions?
Squidward: NO! He cut off his own hand! By mistake!
SpongeBob: You mean like this?
[At every 'this', SpongeBob removes his arm and a new one grows back.]
SpongeBob: Or like this? Or this? Or this? But what about this? Or this? Or this? Or this?
Squidward: Except he wasn't a sponge!
SpongeBob: So?
Squidward: So it didn't grow back!
Answer: I believe this is the Season 6 episode "Spongicus".