cut back vs take away

cut back and take away both are verbs.

Word	Noun	Adjective	Verb	Adverb
cut back	No	No	Yes	No
take away	No	No	Yes	No

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

cut back (verb)	take away (verb)
place restrictions on	take out or remove
cut down on; make a reduction in	remove something concrete, as by lifting, pushing, or taking off, or remove something abstract
cultivate, tend, and cut back the growth of	get rid of something abstract
return in time	take away a part from; diminish
	buy and consume food from a restaurant or establishment that sells prepared food
	remove from a certain place, environment, or mental or emotional state; transport into a new location or state
	take from a person or place