Cut back and start missing paper (4)
I believe the answer is:
exam
'paper' is the definition.
(I've seen this before)
'cut back and start missing' is the wordplay.
'cut' becomes 'axe' (I've seen this before**).
'back' says the letters should be written backwards.
'and' says to put letters next to each other.
'start' suggests taking the first letters.
The first letter of 'missing' is 'm'.
'axe' in reverse letter order is 'exa'.
'exa'+'m'='EXAM'
(Other definitions for exam that I've seen before include "In brief, a test as in school" , "Oral maybe" , "Set of questions evaluating skill or knowledge, in short" , "paper" , "School test (colloq.)" .)