Cut with a whip? (4)
I believe the answer is:
crop
This clue is a double definition.
'cut' is the first definition.
(I know that crop is a more specific form of the action thin out)
'whip' is the second definition.
(crop can mean a whip)
'with a' is the link.
(Other definitions for crop that I've seen before include "Reduce" , "Produce - riding whip" , "Whip with loop instead of lash" , "Yield from cultivation" , "Bird's gullet pouch" .)