The invention relates to a cutting device having a cutting unit for dividing a strip from a material web running in a transport direction relative to the cutting device, and having a base support that defines a cutting section for supporting the material web during the division of the strip, and a supporting section, the supporting section being formed and arranged in such a way that it supports the material web and the strip as they are transported away out of the cutting section in the transport direction, wherein the supporting section has a cutout which extends and is formed in such a way that the cut edge of the material web and/or the cut edge of the strip are not supported on the supporting section, at least in some sections, as they are transported away out of the cutting section.