pull down vs cut down

pull down and cut down both are verbs.

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

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

Other synonyms of pull down include down, knock down, push down.

pull down (verb)	cut down (verb)
cause to come or go down	cut down on; make a reduction in
tear down so as to make flat with the ground	intercept (a player)
	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