cut down vs mow

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

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

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

cut down (noun)	mow (noun)
	a loft in a barn where hay is stored

cut down (verb)	mow (verb)
cut down on; make a reduction in	make a sad face and thrust out one's lower lip
intercept (a player)	cut with a blade or mower
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