The piece of paper is a cutting (4)
I believe the answer is:
slip
I believe this clue is a double definition.
'the piece of paper' is the first definition.
(slip is a kind of piece of paper)
'a cutting' is the second definition.
(I know that cutting can be written as slip)
'is' is the link.
(Other definitions for slip that I've seen before include "Strip" , "Lose footing or make mistake" , "failure" , "Mistake (of tongue or pen)" , "Error - fielder" .)