cut down vs decrease

cut down is not a noun while decrease is a noun.

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

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

Other hypernyms of cut down include lessen, minify.

cut down (noun)	decrease (noun)
	the act of decreasing or reducing something
	the amount by which something decreases
	a change downward
	a process of becoming smaller or shorter

cut down (verb)	decrease (verb)
cut down on; make a reduction in	decrease in size, extent, or range
intercept (a player)	make become smaller
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