drop vs cut down

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

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

As verbs, drop and cut down are synonyms defined as:

Other synonyms of drop include fell, strike down.

drop (noun)	cut down (noun)
the act of dropping something
a central depository where things can be left or picked up
a curtain that can be lowered and raised onto a stage from the flies; often used as background scenery
a sudden sharp decrease in some quantity
a free and rapid descent by the force of gravity
a predetermined hiding place for the deposit and distribution of illicit goods (such as drugs or stolen property)
a steep high face of rock
a small indefinite quantity (especially of a liquid)
a shape that is spherical and small

drop (verb)	cut down (verb)
give birth; used for animals	cut down on; make a reduction in
grow progressively worse	intercept (a player)
go down in value	cause to come or go down
stop pursuing or acting	cut with a blade or mower
change from one level to another	cause to fall by or as if by delivering a blow
lower the pitch of (musical notes)	cut with sweeping strokes; as with an ax or machete
fall or sink into a state of exhaustion or death
leave undone or leave out
omit (a letter or syllable) in speaking or writing
utter with seeming casualness
lose (a game)
take (a drug, especially LSD), by mouth
remove (cargo, people, etc.) from and leave
to remove
cause to fall by or as if by delivering a blow
let or cause to fall in drops
to fall vertically
let fall to the ground
fall or descend to a lower place or level
pay out
stop associating with
terminate an association with
hang loosely