Having conducted surgery, pipes up about working to finish all off ? (4,2,9)
I believe the answer is:
take no prisoners
'finish all off ?' is the definition.
(to kill everyone and thus take no prisoners)
'having conducted surgery pipes up about working' is the wordplay.
'having conducted' becomes 'taken' (having taken is having conducted).
'surgery' becomes 'op' (short for operation).
'pipes up' becomes 'risers' (pipes which rise up).
'about' indicates putting letters inside.
'working' becomes 'on'.
'risers' enclosing 'on' is 'risoners'.
'taken'+'op'+'risoners'='TAKE NO PRISONERS'
'to' is the link.
(Other definitions for take no prisoners that I've seen before include "reduce numbers held in gaol?" , "Ruthlessly pursue aim" .)