An apparatus for forming a wound roll of discrete overlapping sheets of web from a supply of continuous web. The web preferably is passed around a nip roller that steers the web onto the surface of a take-up core. A knife assembly including a knife blade extended from a knife holder is driven by a traversing mechanism across the width of the web to cut the wound web on the core into discrete sheets, the extended height of the knife blade being preferably the exact thickness of the web. In transverse cutting by the knife of the web wound on the take-up core, the knife holder travels on the outer surface of the web, thus assuring that the knife blade extends just to the outer surface of the next inner convolution of web, thereby cutting the continuous web into sheets without damaging previously wound web convolutions.