Cutting apart from around the rear end (7)
I believe the answer is:
excerpt
'cutting' is the definition.
(something extracted or cut from a text)
'apart from around the rear end' is the wordplay.
'apart from' becomes 'except' (I've seen this in another clue).
'around' is an insertion indicator.
'end' says to take the final letters.
The last letter of 'rear' is 'r'.
'except' going around 'r' is 'EXCERPT'.
(Other definitions for excerpt that I've seen before include "Just a few words" , "scrap?" , "Passage from literature or music" , "Short passage" , "part of programme" .)