cut back vs shave

cut back is not a noun while shave is a noun.

Word	Noun	Adjective	Verb	Adverb
cut back	No	No	Yes	No
shave	Yes	No	Yes	No

As verbs, shave is a hyponym of cut back; that is, shave is a word with a more specific, narrower meaning than cut back:

cut back (noun)	shave (noun)
	the act of removing hair with a razor

cut back (verb)	shave (verb)
place restrictions on	remove body hair with a razor
cut down on; make a reduction in	touch the surface of lightly
cultivate, tend, and cut back the growth of	cut closely
return in time	cut or remove with or as if with a plane
	make shavings of or reduce to shavings
	cut the price of