take away vs cut back

take away and cut back both are verbs.

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

As verbs, cut back is a hypernym of take away; that is, cut back is a word with a broader meaning than take away:

Other hypernyms of take away include bring down, cut, cut down, reduce, trim, trim back, trim down.

take away (verb)	cut back (verb)
take out or remove	place restrictions on
remove something concrete, as by lifting, pushing, or taking off, or remove something abstract	cut down on; make a reduction in
get rid of something abstract	cultivate, tend, and cut back the growth of
take away a part from; diminish	return in time
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