To provide a beveling device which can relax machine rigidity and form a total constitution in a small size, by devising a constitution of a clamp means.

In a beveling device fixedly pressing a workpiece W supplied onto a table by many clamp means C1 to Cn also cutting this workpiece by a cutter moved to run in the same direction to an arrangement direction of the clamp means, the clamp means C1 to Cn is constituted by a hydraulic cylinder 171 to 17n, low and high pressure oil is switched to be supplied thereto. This hydraulic cylinder 171 to 17n, corresponding to a running movement position of a cutting head 6, is set to a high pressure side in the vicinity of a cutting position of a cutter 9, and to a low pressure side except in that position. In this way, total unit thrust of the hydraulic cylinder 171 to 17n is reduced.