Synonyms for Cut down:

n.

give in, abandon, break a habit, swear off, yield, give up, grow out of, kick. append, adapt, dramatize, compress, condense, bowdlerize, delete, censor. arboretum, afforestation, forester, clear-cut, coppice, arboriculture, defoliate, chop down. lead to, influence, color, grip, pack a punch, give, decide, catch, skew, stir. bump off, assassinate, take someone's life, massacre, slaughter, dispatch, strangle, exterminate. halve, minimize, erode, decrease, top-slice, shrivel. cut down (noun)
pull down, reduce, felled, downed, strike down, trim down, trim back, bring down, trim, cut, push down, slash, drop, mow, fell, cut back, down.

v.

change (verb)
cut, cut back, trim back, trim down, reduce, bring down, trim.
fell (verb)
mow, dispatch, slaughter, massacre.

Other synonyms:

coppice, dramatize, clear-cut, bowdlerize, give in, grow out of, yield, afforestation, swear off, append, defoliate, forester, censor, condense, chop down, arboretum, arboriculture. give up, compress, kick, delete. adapt. dispatch, abandon. decrease
downed.
economize
cut back.
Other relevant words:
minimize, dispatch, compress, decrease, slaughter, cut, condense, chop down, exterminate, massacre.