If you turn it over, you'll see a cover over the magnet. Might be foil, might be thin plastic. The magnet itself is a ring, and there will be an empty hole in the center. You can try cutting out the center. That should give you access to two screws. Unscrew those and the NMO mount should come right off. You should be able to resolder the coaxial cable to the connector. You can try putting a ty-wrap around the coax to keep it from pulling out again. Reassemble and you should be good to go.
If it's a cheap Chinese antenna mount, your guess is as good as mine. Might be a total knock off of the Laird, or may be completely different.