cut down vs cut back

cut down and cut back both are verbs.

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

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

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

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