trimming vs cutting off

trimming and cutting off both are nouns.

Word	Noun	Adjective	Verb	Adverb
trimming	Yes	No	No	No
cutting off	Yes	No	No	No

As nouns, cutting off is a hypernym of trimming; that is, cutting off is a word with a broader meaning than trimming:

Other hypernyms of trimming include cut, cutting.

trimming (noun)	cutting off (noun)
the act of adding decoration	the act of shortening something by chopping off the ends
cutting down to the desired size or shape	the act of cutting something off
a decoration or adornment typically on the edge of a garment