strike vs cut down

strike is a noun but cut down is not a noun.

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

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

strike (noun)	cut down (noun)
a group's refusal to work in protest against low pay or bad work conditions
a score in tenpins: knocking down all ten with the first ball
an attack that is intended to seize or inflict damage on or destroy an objective
a conspicuous success
(baseball) a pitch that the batter swings at and misses, or that the batter hits into foul territory, or that the batter does not swing at but the umpire judges to be in the area over home plate and between the batter's knees and shoulders
a gentle blow

strike (verb)	cut down (verb)
cause to form (an electric arc) between electrodes of an arc lamp	cut down on; make a reduction in
arrive at after reckoning, deliberating, and weighing	intercept (a player)
indicate (a certain time) by striking	cause to come or go down
make a strategic, offensive, assault against an enemy, opponent, or a target	cut with a blade or mower
deliver a sharp blow, as with the hand, fist, or weapon	cause to fall by or as if by delivering a blow
hit against; come into sudden contact with	cut with sweeping strokes; as with an ax or machete
affect or afflict suddenly, usually adversely
produce by manipulating keys or strings of musical instruments
remove by erasing or crossing out or as if by drawing a line
pierce with force
smooth with a strickle
hook by a pull on the line
produce by ignition or a blow
form by stamping, punching, or printing
disassemble a temporary structure, such as a tent or a theatrical set
have an emotional or cognitive impact upon
drive something violently into a location
occupy or take on
cause to experience suddenly
find unexpectedly
stop work in order to press demands
attain
touch or seem as if touching visually or audibly