Cut causing many a cry of pain (3)
I believe the answer is:
mow
'cut' is the definition.
(as in mowing a lawn)
'many a cry of pain' is the wordplay.
'many' becomes 'm' (Roman numeral for a thousand).
'a cry of pain' becomes 'ow' (exclamation of pain).
'm'+'ow'='MOW'
'causing' acts as a link.
(Other definitions for mow that I've seen before include "'Cut down, hay, say (3)'" , "'Cut, grass say (3)'" , "Cut grass on lawn" , "Cut (e.g. grass)" , "Cut grass or grain" .)