Clean injured daughter's cut (6)
I believe the answer is:
lanced
'cut' is the definition.
(lancing is a kind of cutting)
'clean injured daughter's' is the wordplay.
'injured' indicates an anagram.
'daughter' becomes 'd' (genealogical abbreviation).
'clean' with letters rearranged gives 'lance'.
'lance'+'d'='LANCED'
(Other definitions for lanced that I've seen before include "Pierced surgically as with boil" , "Pierced with a knife" , "Cut open as surgeon did a boil" .)