As pointed out above the damaged cable probably resulted in a short and damage to one or more of the hall sensors in the motor. so even a perfect repair of the damaged cable will still leave you with the problem.
the hall sensors are easy to diagnose and repair, (
https://ebikes.ca/documents/HallSensorTestingFinal.pdf ) you may even find a plug in replacement pcb on ebay for a fiver.
Look at the motor cable ads linked to above match one to yours, in both length and connecting ends. If really stuck pull your cable take photos and post here for direction. the motor end will be either 3x or 9x round connector in most cases and the controller/sensor end will either be julet waterproof connectors or more generic automotive style smt connectors. And since you can solder if one or two connections dont match (unlikely) .. the point of a new cable is removing uncertainty with a possibly damaged cable.