This language of man’s being cut off is covenantal language. Covenants were initiated by a cutting ritual. In Genesis 15:1–21 God established his covenant with Abram by having Abram bring him some animals, cut them in half, and lay each half over against the other. After sundown, with Abram in a deep sleep, the Lord passed between the pieces, thereby establishing a covenant with Abram. Although our English Bibles usually translate this as, He made/established a covenant,
the Hebrew literally says, He cut a covenant.
Walking between the pieces was to communicate, I promise to live for you, and if I don't live for you, may what happened to these animals happen to me—that I be cut off.
So if one or other of the parties failed to keep their promises, they would be cut off. That is now what seems to be in view in Zephaniah 1:3: the cutting off, indeed, the cursing of mankind for failure to keep covenant with the Lord—whether that be all creation (Noahic covenant) or God’s chosen people (Abrahamic covenant).
3 “I will sweep away man and beast; I will sweep away the birds of the heavens and the fish of the sea, and the rubble with the wicked. I will cut off mankind from the face of the earth,” declares the LORD.