cut down vs lessen

cut down and lessen both are verbs.

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

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

Other hypernyms of cut down include decrease, minify.

cut down (verb)	lessen (verb)
cut down on; make a reduction in	decrease in size, extent, or range
intercept (a player)	wear off or die down
cause to come or go down	make become smaller
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