A cutting machine for processing workpieces using a rotating cutting wheel, comprising: a cutting wheel and a drive motor for driving the cutting wheel; a work table for fixing a workpiece to be processed, the work table defining an x-z-plane; a first displacement means for producing a relative displacement between the workpiece and the cutting wheel in a first direction in the x-z-plane in order to position the workpiece for separating cuts with the cutting wheel in the first direction in the x-z-plane relative to the cutting wheel; a workpiece positioning device including a clamping means for clamping the workpiece and a first mechanical rotating means for rotatably positioning the workpiece clamped in the clamping means about a first rotation axis prior to or between performing separating cuts, said first rotation axis extending perpendicular to the x-z-plane; a machine housing which accommodates the cutting wheel, the work table and the workpiece positioning device and defines a working space, wherein the machine housing includes a covering hood which closes the working space during the performing of the separating cuts and allows the user to access the workpiece positioning device and the workpiece prior to and after the performing of the separating cuts; a lifting mechanism for setting the cutting wheel on the workpiece in y-direction perpendicular to the x-z-plane for performing separating cuts in the workpiece using the cutting wheel; and a program controller with control of the first rotating means integrated therein, so that the program controller automatically controls the relative displacement in the first direction and the rotation of the workpiece about the first rotation axis prior to and between separating cuts, so that a plurality of separating cuts are automatically controlled successively at different positions in the x-z-plane and with different rotational positions of the workpiece. a cutting wheel and a drive motor for driving the cutting wheel; a work table for fixing a workpiece to be processed, the work table defining an x-z-plane; a first displacement means for producing a relative displacement between the workpiece and the cutting wheel in a first direction in the x-z-plane in order to position the workpiece for separating cuts with the cutting wheel in the first direction in the x-z-plane relative to the cutting wheel; a workpiece positioning device including a clamping means for clamping the workpiece and a first mechanical rotating means for rotatably positioning the workpiece clamped in the clamping means about a first rotation axis prior to or between performing separating cuts, said first rotation axis extending perpendicular to the x-z-plane; a machine housing which accommodates the cutting wheel, the work table and the workpiece positioning device and defines a working space, wherein the machine housing includes a covering hood which closes the working space during the performing of the separating cuts and allows the user to access the workpiece positioning device and the workpiece prior to and after the performing of the separating cuts; a lifting mechanism for setting the cutting wheel on the workpiece in y-direction perpendicular to the x-z-plane for performing separating cuts in the workpiece using the cutting wheel; and a program controller with control of the first rotating means integrated therein, so that the program controller automatically controls the relative displacement in the first direction and the rotation of the workpiece about the first rotation axis prior to and between separating cuts, so that a plurality of separating cuts are automatically controlled successively at different positions in the x-z-plane and with different rotational positions of the workpiece.