Parent gets cut up by surgeon's saw (6)
I believe the answer is:
trepan
'surgeon's saw' is the definition.
'parent gets cut up' is the wordplay.
'gets cut up' is an anagram indicator.
'parent' with letters rearranged gives 'TREPAN'.
'by' is the link.
(Other definitions for trepan that I've seen before include "Surgical saw" , "Perforate skull (med.)" , "Cranial surgical instrument" , "Skull borer" , "Make perforation in person's skull" .)