PURPOSE: To provide a machine for cutting off a tube part from a tube, capable of quickly and easily performing chamber of the outer and inner edges of a cut surface after cutting-off of the tube part.

CONSTITUTION: A machine for cutting off a tube part 7b from a tube 7 is provided with a surface plate 30 to be rotationally driven between two chuck devices 5, 9, and a cutting-off tool 38 and a chamfering tool 46 are radially movably arranged on the front end surface. Since the chamfering tool 46 can be axially moved in relation to the surface plate, it can be moved to the inside of the tube beyond the cut surface of the storage length 7a of the pipe 7 to chamfer the inner edge of the cut surface.