haircut vs cutting off

haircut and cutting off both are nouns.

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

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

Other hypernyms of haircut include cut, cutting.

haircut (noun)	cutting off (noun)
the act of cutting the hair	the act of shortening something by chopping off the ends
the style in which hair has been cut	the act of cutting something off