A web of paper, cardboard, foil or textile material is pulled against and between two rotary knives which sever the web longitudinally and form a slot as well as dust. Such dust is removed by a pneumatic mechanism having one or more nozzles which discharge one or more streams of compressed ionized air against the upper side of the web in the region of the slot, and a suction chamber disposed beneath the path for the web, extending across the slot beneath the nozzle or nozzles, and having one or more suction ports which enable the chamber to collect the particles of dust. The port or ports further enable the chamber to collect those fragments of the web which adhere to the separated sections of the web in the region of the slot between such sections.