To realize the technique to easily cut a pipe along a desired cutting line.

This cutting device is provided with a first mold 40 having a restriction edge 40A extended along the desired cutting line of the pipe and restricting one side with respect to the desired cutting line of the pipe, a second mold 44 opposite to the first mold 40 through a clearance C and restricting the other side with respect to the desired cutting line of the pipe, and a displacement means for repeatedly finely displacing the second mold 44 to the first mold 40 within an allowable range of the clearance C. One side with respect to the desired cutting line of the pipe is restricted by the mold having the restriction line extended along the desired cutting line of the pipe, and the other side with respect to the desired cutting line can be repeatedly finely displaced to one side. The fatigue of a pipe material is concentrated and advanced on a part along a boundary (restriction edge) where the pipe is restricted by the mold, and the pipe is cut along the restriction edge by fatigue fracture.