Share a cut and many tear up (5)
I believe the answer is:
shred
'tear up' is the definition.
(synonyms)
'share a cut and many' is the wordplay.
'cut' is a deletion indicator.
'and' says to put letters next to each other.
'many' becomes 'd'.
'share' with 'a' removed is 'shre'.
'shre'+'d'='SHRED'
(Other definitions for shred that I've seen before include "Cut into bits" , "Tiny amount" , "Small piece torn from something" , "Scrap; finely tear" , "Small part" .)