Chilled and cut up, with head removed (4)
I believe the answer is:
iced
'chilled' is the definition.
(icing is a kind of chilling)
'cut up with head removed' is the wordplay.
'cut up' becomes 'diced' (I've seen this before).
'with head removed' means to remove the first letter.
'diced' with its first letter taken off is 'ICED'.
'and' acts as a link.
(Other definitions for iced that I've seen before include "Decorated (a cake)" , "Took out" , "Chilled; decorated" , "hidden under white crystals?" , "Decorated; killed" .)