Points to serious cut (7)
I believe the answer is:
engrave
'cut' is the definition.
(I know that engrave is a type of chip at)
'points to serious' is the wordplay.
'points' becomes 'en' ().
'to serious' becomes 'grave' (both can mean solemn).
'en'+'grave'='ENGRAVE'
(Other definitions for engrave that I've seen before include "impress deeply" , "Cut or carve (a design)" , "Carve (a design) into hard material" , "Carve into surface as of medal" , "Avenger (anag) - chase" .)