Cook cut unimportant piece of game (6)
I believe the answer is:
domino
'piece of game' is the definition.
(piece used in the game of dominoes)
'cook cut unimportant' is the wordplay.
'cook' becomes 'do' (I've seen this in other clues).
'cut' means to remove the last letter.
'unimportant' becomes 'minor'.
'minor' with its final letter removed is 'mino'.
'do'+'mino'='DOMINO'
(Other definitions for domino that I've seen before include "Spotted playing tile" , "Piece with pips; Fats ---, R&B singer" , "one's spotted" , "Small rectangular tile with varying numbers of spots" , "Black and white game piece" .)