Unfortunately we had some of the pins break on the 393 motors. The rules state that identical VEX wires must be used, would that mean that severing the third cable on a 3 wire connector is also legal? Or would it be necessary to get the wires from a broken 393, or purchase the 2 wire extension cables?
This is not legal. It would be violation of <R15a>:
VEX Robotics Competition Nothing But Net Game Manual:
<R15> Parts may NOT be modified as follows:
a. Motors (including the internal PTC), extension cords, sensors, controllers, battery packs, reservoirs, solenoids, pistons and any other electrical component or pneumatics component of the VEX Robotics Design System may NOT be altered from their original state in ANY way.
You are correct, this would be the legal way to repair your motor, as per
VEX Robotics Competition Nothing But Net Game Manual:
ii. External wires on VEX electrical components may be repaired by soldering, using twist/crimp connectors, electrical tape or shrink tubing such that the original functionality / length is not modified in any way. Wire used in repairs must be identical to VEX wire. Teams may make these repairs at their own risk; incorrect wiring may have undesired results.