A corrugating apparatus comprises at least one device for producing an at least single-faced corrugated web transported along a transport direction, at least one cross-cutting device disposed downstream thereof along the transport direction for cutting the corrugated web and at least one discharge device for discharging waste pieces of the corrugated web perpendicular to the transport direction, wherein the discharge device comprises at least one controllably movable deflector element which is engageable with the waste pieces to be discharged.