knock off vs cut down

knock off and cut down both are verbs.

Word	Noun	Adjective	Verb	Adverb
knock off	No	No	Yes	No
cut down	No	No	Yes	No

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

Other hypernyms of knock off include bring down, cut, cut back, reduce, trim, trim back, trim down.

knock off (verb)	cut down (verb)
stop pursuing or acting	cut down on; make a reduction in
get rid of (someone who may be a threat) by killing	intercept (a player)
write quickly	cause to come or go down
take by theft	cut with a blade or mower
cut the price of	cause to fall by or as if by delivering a blow
	cut with sweeping strokes; as with an ax or machete