The device comprises a casing, with a passage for introduction of an end portion of the sheathed wires, a catch for receiving the said end portions in the casing, a clip (12) arranged to be introduced into the casing transversely to the sheathes, with at least two slots (13) to grip the sheathes of the wires and to draw them towards the inside and the bottom of the casing and arranged to cooperate with the catch in order to strip the wires. Spacing means (52, 53) are also provided between the catch and the gripping and drawing clip (12) to keep their spacing greater than a cutting threshold.