PURPOSE: To enable a work to be efficiently cut off without any deformation by providing a swinging device for adding swing movement to the work except for in the cutting direction of a grinding wheel in order to cut off the work while swinging said device.

CONSTITUTION: A swinging frame 12 carries out circular movement in a vertical plane about the rotational center of an eccentric shaft 20 which is rotated by a motor 26, so that a cutting grinding wheel 30 moving integrally with the swinging frame 12 moves forward/backward and up/down in the cut plane in relation to a work. The vertical movement of the wheel 30 is almost absorbed by swing about the axis of the eccentric shaft 20 so that the cutting grinding wheel 30 will move principally forward and backward. Thus, the cutting grinding stone 30 moves forward and backward along the cutting surface and cuts gradually the cutting surface while cutting same in the cutting direction of swing about the axis of the eccentric shaft 20 as a whole so that the work can be efficiently cut off without deformation.