To prevent a short material from moving during cutting machining by stabilizing a nip and hold condition of the short material by a main body vice device even if a part to be nipped and held in the short material is small.

A machining head which cuts a section to be cut of a material W at a cutting position and is provided with a cutting blade 9 is provided, a main body vice device 11 nipping and holding the vicinity of the section to be cut of the material at the time of cutting machining is provided, a conveyance vice device 21 is provided on one side of this main body vice device 11 so as to move in the forward and backward directions in which it approaches and leaves the main body vice device 11, and a knocking member 33 against which an end face of the short material W can be knocked is provided in this conveyance vice device 21.