A cutting - a piece of paper (4)
I believe the answer is:
slip
I believe this is a triple definition!
'a cutting' is the first definition.
(I know that cutting can be written as slip)
'a piece' is the second definition.
(thesaurus)
'of' acts as a link.
'paper' is the third definition.
(slip is a kind of paper)
(Other definitions for slip that I've seen before include "Nod" , "Cutting" , "Sole lapse" , "Lose footing as on banana skin" , "Cricket fielder - mistake" .)