Fight and cut domineering woman (6-3)
I believe the answer is:
battle-axe
'domineering woman' is the definition.
(I've seen this before)
'fight and cut' is the wordplay.
'fight' becomes 'battle' ('battle' can be a synonym of 'fight').
'and' means one lot of letters go next to another.
'cut' becomes 'axe' (I've seen this before).
'battle'+'axe'='BATTLE-AXE'
(Other definitions for battle-axe that I've seen before include "Overbearing woman" , "Large broad-bladed weapon" , "Ancient combat weapon or very tough woman" , "Broad-bladed weapon - domineering woman" , "Old chopper- nagging old woman" .)