Terribly crude joke finally cut (6)
I believe the answer is:
reduce
'cut' is the definition.
(I know that cut can be written as reduce)
'terribly crude joke finally' is the wordplay.
'terribly' indicates anagramming the letters.
'finally' suggests the final letters.
The final letter of 'joke' is 'e'.
'crude' anagrammed gives 'reduc'.
'reduc'+'e'='REDUCE'
(Other definitions for reduce that I've seen before include "Subjugate; make (sauce) thicker" , "Make or become smaller" , "diet" , "Lower" , "Shrink" .)