cut back vs cut down

cut back and cut down both are verbs.

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

As verbs, cut back and cut down are synonyms defined as:

Other synonyms of cut back include bring down, cut, reduce, trim, trim back, trim down.

cut back (verb)	cut down (verb)
place restrictions on	cut down on; make a reduction in
cut down on; make a reduction in	intercept (a player)
cultivate, tend, and cut back the growth of	cause to come or go down
return in time	cut with a blade or mower
	cause to fall by or as if by delivering a blow
	cut with sweeping strokes; as with an ax or machete