Leaves the half dead bits (7)
I believe the answer is:
departs
'leaves' is the definition.
('depart' can be a synonym of 'leave')
'half dead bits' is the wordplay.
'half' suggests halving the letters.
'bits' becomes 'parts' (I've seen this before).
'dead' cut in half is 'de'.
'de'+'parts'='DEPARTS'
'the' acts as a link.
(Other definitions for departs that I've seen before include "Goes, leaves" , "Quits" , "Does runner" , "Goes away" .)