cut down vs pull down

cut down and pull down both are verbs.

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

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

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

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