retrench vs cut down

retrench and cut down both are verbs.

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

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

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

retrench (verb)	cut down (verb)
make a reduction, as in one's workforce	cut down on; make a reduction in
tighten one's belt; use resources carefully	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