PURPOSE: To provide a rotary grinding wheel device without causing any large burr in a cutting end part at cutting of material, extremely easy in handling, and dispensing with additional working.

CONSTITUTION: Material W is fed to the parallel direction to a grinding wheel 1 turning vertically and cut in a rotary grinding wheel device. The device has a receiving member 2 which has a receiving part 2a for supporting a bottom of a cutting end part W2 when the material W is cut and an actuating cylinder 3 for lifting up and down the receiving member from an upper position where the receiving part supports the bottom of the cutting end part to a position lower than this position and a control member for controlling the actuating cylinder such that the receiving member 2 gradually rises when the material is cut and it comes to the upper position when the cutting is nearly finished.