or 'resistance-type wire-rope parting machine', although there may be a shorter name (!)

ref:

How is the rope parted?
The wire rope parting process is achieved by passing a large current through a small section of the rope, and using its own electrical resistance to provide sufficient heat to melt it. When properly controlled (tie melted section separates and the parted strands surrounding the break are welded together with virtually no increase in rope diameter.

Machine Operation

An adjustable feed mechanism pulls the specified length of rope from a decoiler or similar device. This same mechanism simultaneously pushes the rope between the electrodes that are closed encompassing the rope to complete the secondary circuit.

Since the wire rope is used as the load to complete the secondary electrical circuit the resistance of the rope multiplied by the current delivered from the controller, will determine the power dissipated in the portion of wire rope between the electrodes. Providing sufficient power for a certain time causes the wire rope to melt.

Therefore by judicious balance between the volume of rope, electrode gap and the configured electrical power supplied, very accurate cutting of the wire is achieved.

http://www.fpe.co.uk/wirerope.htm