PURPOSE: To prevent the generation of chipping on a workpiece and clogging caused by a wrapping member by covering the workpiece with a wrapping member before cutting the workpiece with a cutting grinder while rotating the workpiece.

CONSTITUTION: The outer periphery 8 of a column-shaped workpiece 1 is covered with a wrapping member 9. The workpiece 1 covered with the wrapping member 9 is arranged to move to a thin internal periphery type grinder 3 and is cut with the grinder 3 while rotating the workpiece 1, and at a place near a rotary axis line 2, the rotation of the workpiece 1 is stopped. An uncut portion 10 is cut so as to obtain a thin member 11 by merely moving the workpiece 1. The grinder 3 cuts into the wrapping member 9. Being transferred sequentially, the grinder 3 comes into contact with the workpiece 1. As the workpiece 1 is covered with a wrapping member 8, however, chipping 5 is not generated.