(formal) to kill somebody He was cut down by an assassin's bullet.
to make something fall down by cutting it at the base to cut down a tree See related entries: Gardening
to reduce the size, amount or number of something We need to cut the article down to 1 000 words. The doctor told him to cut down on his drinking. I won't have a cigarette, thanks—I'm trying to cut down (= smoke fewer).