Refuse and go off depressed (4,4)
I believe the answer is:
turn down
'refuse' is the definition.
(turning down is a kind of refusing)
'go off depressed' is the wordplay.
'go off' becomes 'turn' (I've seen this before).
'depressed' becomes 'down' (synonyms).
'turn'+'down'='TURN-DOWN'
'and' acts as a link.
(Other definitions for turn down that I've seen before include "Reject - reduce volume" , "mark the place" , "Refuse - to reduce the volume" , "Dim - reject" , "prepare bed" .)