Abstract: The device comprises a support (11) equipped with a fastening element, an assembly (12) mounted movably relative to the support (11) in the direction of the axis (8) of the tubular piece, a pole (13) mounted in the assembly (12) in the direction of the axis (8), an electrode holder (14) in several parts, and an actuating rod mounted movably in the pole (13) in the direction of the axis (8), in order to ensure the spacing of the various parts of the electrode-holder (14) and the radial movement of the electrodes. A vibrator (16) enables vibration of the pole (13) and the electrode-holder (14) in the direction of the axis (8). In a first phase, the wall of the tubular piece is pierced as a result of the radial movement of the electrodes, and in a second phase, cutting is carried out as a result of the axial movement of the movable assembly (12) carrying the pole (13).