If you've been able to pull some of the cable into the box that is intact, I would cut off the damaged part and then use these butt splices to attach some new wire to connect to the receptacle.
https://www.homedepot.com/p/Ideal-S...sh-In-Butt-Splices-10-Pack-30-1342S/202894306
The thing that would worry me is what shape is the cable in outside the box, that you can't see?
https://www.homedepot.com/p/Ideal-S...sh-In-Butt-Splices-10-Pack-30-1342S/202894306
The thing that would worry me is what shape is the cable in outside the box, that you can't see?