A pyrotechnic cut-off device to be connected to an electrical circuit to cut-off, includes a pyrotechnic initiator, a first and a second conductive portion each intended to be connected to the electrical circuit, the second portion being connected in parallel with the first portion and including two conductive elements separated by an insulating segment, at least one of the conductive elements provided with a first fuse element connected in series which is configured to trip when the intensity of the current passing therethrough exceeds a first predetermined value, and a first and a second insulating protrusion, each protruding from a lower face of a movable piston and the first and the second protrusions being located respectively in front of the first portion and the insulating segment. The pyrotechnic initiator is configured to switch the cut-off device from a first current passage configuration to a second current cut-off configuration.