A disc cutting apparatus for cutting opposite surfaces of a disc-shaped workpiece such as a disc rotor for an automobile disc brake includes a rotating mechanism for positioning and rotating the workpiece which is pressed, under uniform pressure, radially inwardly by a plurality of holder mechanisms. While the workpiece is being rotated by the rotating mechanism and pressed by the pressing mechanism, the workpiece is cut by a cutting mechanism. The cutting mechanism includes cutters for cutting opposite surfaces of the workpiece, and the cutters are positionally adjusted with respect to the workpiece based on positional information detected by a detector which has a probe held against the workpiece.