detract vs cut down

detract and cut down both are verbs.

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

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

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

detract (verb)	cut down (verb)
take away a part from; diminish	cut down on; make a reduction in
	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