A disc screen apparatus is disclosed for separating mixed recyclable materials of varying sizes and shapes. The disc screen apparatus has an enclosure or frame with an input, a container discharge location and a paper discharge location. A first plurality of shafts and second plurality of shafts are rotatably supported by the frame. The first plurality of shafts form a first disc screen disposed in a first plane and the second plurality of shafts form a second disc screen at least a portion of which is disposed in a second plane. The second plane is disposed beneath and angled with respect to the first plane such that the planes at least partially overlap. One or more motors rotate the first and second plurality of shafts. Each shaft has a plurality of discs positioned along it. The discs are offset between adjacent shafts such that discs on each shaft interleave with discs on an adjacent shaft but do not touch the adjacent shaft. The discs are substantially square in shape with radiused corners. The radiused corners have a texture, such as ridges. The arrangement of the discs on the shafts creates a screening pattern capable of screening a portion of the mixed recyclable materials. Each disc is assembled about a shaft from two identical portions. The portions are clamped together, about the shaft to form the disc. If the disc is damaged or worn, it may be removed from the shaft for repair or replacement without disassembly of the shaft from the apparatus or removal of other discs. The discs are also disclosed as comprising an inner rigid frame supporting an outer, softer material.