Police officer's personal cut (6)
I believe the answer is:
disown
'cut' is the definition.
(cut can mean to disown or ignore socially)
'police officer's personal' is the wordplay.
'police officer's' becomes 'DI's' (abbreviation for Detective Inspector).
'personal' becomes 'own' (eg one's own possessions are personal possessions).
'dis'+'own'='DISOWN'
(Other definitions for disown that I've seen before include "Disclaim or deny" , "Reject all connection or relationship with" , "Refuse to be associated with (something/someone)" , "Refuse to be associated with (a person)" , "Repudiate or refuse to acknowledge a relationship" .)