Apocryphal story very much shortened (5)
I believe the answer is:
tobit
'apocryphal story' is the definition.
(Book of Tobit, apocryphal book of the Bible)
'very much shortened' is the wordplay.
'very much' becomes 'to bits ' (I've seen this before).
'shortened' means to remove the last letter.
'tobits' with its last letter taken away is 'TOBIT'.
(Other definitions for tobit that I've seen before include "Good book" , "Old Testament character" , "apocryphal book" , "Book of the Apocrypha" .)