An inner peripheral cutting edge (10) is made of a doughnut-shaped blade (12) deposited diamond grains, arranged rotatably in the directionof an arrow and held in a moving trestle (16). The moving trestle (16) is mounted movable in the direction of an arrow B along rails (18 and 18) located in sides of the inner peripheral cutting edge (10), and driven by instruction signals from a control section (20). A workpiece (22) is placed at the inner peripheral position of the inner peripheral cutting edge (10) and rocked about the axis thereof by a motor (25). The motor (25) is fitted on a beam member and driven by instruction signals from the control section (20). With this arrangement, the inner peripheral cutting edge (10) is rotated in the direction of the arrow A, and then the moving trestle (16) is fed in the direction of the arrow B by the control section (20) and the workpiece (22) is pressed against a grindstone (14) of the inner peripheral cutting edge (10), sthat the workpiece (22) is cut by a predetermined value, thereafter, the moving trestle (16) is stopped by the control section (20) and the workpiece (22) is rocked about the axis thereof by driving the motor (25), so that a reminder part can be cut.