cut down vs take away

cut down and take away both are verbs.

Word	Noun	Adjective	Verb	Adverb
cut down	No	No	Yes	No
take away	No	No	Yes	No

As verbs, take away is a hyponym of cut down; that is, take away is a word with a more specific, narrower meaning than cut down:

cut down (verb)	take away (verb)
cut down on; make a reduction in	take out or remove
intercept (a player)	remove something concrete, as by lifting, pushing, or taking off, or remove something abstract
cause to come or go down	get rid of something abstract
cut with a blade or mower	take away a part from; diminish
cause to fall by or as if by delivering a blow	buy and consume food from a restaurant or establishment that sells prepared food
cut with sweeping strokes; as with an ax or machete	remove from a certain place, environment, or mental or emotional state; transport into a new location or state
	take from a person or place