A sawing machine having a first and a second saw with cutting planes generally perpendicular to each other includes a mechanism for conveying cut planar workpieces from one saw to the other. The mechanism includes a plurality of rows of rollers located adjacent each other and spaced apart with a grate mechanism having grate elements extending between the rows of rollers being movable to transport cut workpieces from a support table of the first saw to the roller rows. A gap formed between the work table of the first saw and the roller rows enables trim waste to fall from the support table, and the grate mechanism is pivotally mounted for reciprocal movement between the support table and the roller rows during which it bridges the gap therebetween.