downsize vs cut down

downsize and cut down both are verbs.

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

As verbs, cut down is a hypernym of downsize; that is, cut down is a word with a broader meaning than downsize:

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

downsize (verb)	cut down (verb)
(of a company) reduce in size or number of employees	cut down on; make a reduction in
design or manufacture in a smaller size	intercept (a player)
dismiss from work	cause to come or go down
	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