The transporting roller, which serves for transporting a web of material which is wound up onto a winding shaft, is provided with a cutting device, which comprises a cutter and a cutter holder. The transporting roller has a groove, in which the cutter is guided. A catching device permits the introduction of the cutter into the groove. The groove is inclined with respect to an axially parallel generatrix, so that the web of material is cut off at an oblique angle.