Cut is almost serious (5)
I believe the answer is:
sever
'cut' is the definition.
(severing is a kind of cutting)
'almost serious' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'serious' becomes 'severe' (synonyms).
'severe' with its last letter taken off is 'SEVER'.
'is' is the link.
(Other definitions for sever that I've seen before include "Cut completely" , "Cut right off" , "Divide by cutting" , "Cut off suddenly" , "Cut or break off, perhaps a relationship" .)