A system for cutting generally planar quadrilateral workpieces into a plurality of quadrilateral elements, at least a portion of which have both their length and width dimensions smaller than the overall length and width dimensions of the original workpiece wherein cuts extending completely across the workpiece parallel to one of the length and the width dimensions thereof are first effected by a first saw with the cut pieces being then conveyed to a third saw where cuts completely thereacross may be made in directions perpendicular to the one dimension. The remainder of the workpiece is conveyed to a second saw where cuts are made in directions parallel to the other of the length and width dimensions with the cut portions of the workpiece remainder being subsequently conveyed to the third saw for effecting cuts in the cut portions in directions parallel to the one dimension. The pieces initially cut from the workpiece by the first saw bypass the second saw and instead of being conveyed directly to the third saw they may be conveyed to a storage table for temporary storage after which they may be conveyed to the third saw. The system includes a transfer table which may operate to rotate the bypassed pieces through 90.degree. and to feed the bypassed pieces either directly to the third saw or to the storage table for subsequent feeding from the storage table to the third saw.