Having cut off tails, has to dispose of shellfish (6)
I believe the answer is:
mussel
'shellfish' is the definition.
(I know that mussel is a type of shellfish)
I don't understand the remainder of the clue.
(Other definitions for mussel that I've seen before include "Black marine bivalve" , "Common edible marine mollusc" , "Shellfish sounds like part of the body" , "Edible bivalve mollusc, common in sea" , "The shellfish sounds strong" .)