Cut is acute cut (5)
I believe the answer is:
sever
'cut' is the definition.
(severing is a kind of cutting)
'acute cut' is the wordplay.
'acute' becomes 'severe' ('severe' can be a synonym of 'acute').
'cut' means to remove the last letter.
'severe' with its last letter removed is 'SEVER'.
'is' is the link.
(Other definitions for sever that I've seen before include "Cut into parts" , "Disconnect" , "Cut apart, maybe a relationship" , "Cut or break off, perhaps a relationship" , "Divorce" .)