A device for processing a continuous web includes a feed station for feeding the web in a feed direction towards a cutting station for cutting the web to a cutting length into individual segments of web that are disc-shaped. A further feed station feeds each segment. A first cutting unit cuts the web into the segments and a second cutting unit includes a cutting element configured to sever the web across a full width in a direction transverse to the feed direction. A drive unit is configured to issue a command to move the cutting element from a non-operating position, where the web is fed by the feed station to the first cutting unit through the second cutting unit, to an operating position, where the web is severed by the cutting element to interrupt feeding of the web to the first cutting unit.