A device for cutting the umbilical cord (3) of a torpedo (4), and having: a substantially flat rotary member (10) defining a peripheral cutting portion (13) and having a hinge hole (14) by which to hinge it to an outer surface of the torpedo (4); and a flap (16) connected to the substantially flat rotary member (10) and defining an eye (17) through which to thread the umbilical cord (3). The flap (16) is movable between a raised work position, in which the flap (16) is crosswise to the substantially flat rotary member, and a withdrawn rest position, in which the flap (16) is substantially coplanar with the substantially flat rotary member (10).