Point in a cutter surprisingly cut! (8)
I believe the answer is:
truncate
'cut' is the definition.
(I know that truncate is a type of shorten)
'point in a cutter surprisingly' is the wordplay.
'point' becomes 'n' (N is an example).
'in' indicates putting letters inside.
'surprisingly' is an anagram indicator (a surprising ordering of the letters).
'a'+'cutter'='acutter'
'acutter' anagrammed gives 'trucate'.
'n' going inside 'trucate' is 'TRUNCATE'.
(Other definitions for truncate that I've seen before include "Shorten by cutting off the top" , "Cut short" , "Dock" , "Make shorter by cutting off" , "Lop" .)