To repair an accelerator cable, or throttle cable, remove the tubing; cut, sand and drill it; and then prepare it to go back into the engine. The final step is to solder it back to the throttle.
To remove the accelerator cable, open the hood of the car, and pull the throttle arm down to loosen the cable. Ease the cable from the body with a screwdriver, and when it is free, remove the pins from the gas pedal and the body. Once it is totally free from the engine, pull the cable out.
Using a tubing cutter, cut about an inch of copper tubing. Sand the tubing inside out, which helps to remove oxides that could affect the soldering outcome. Use a small drill bit and drill a small hole 1/8 of an inch away from the end. Make sure that the hole only goes through one side of the tubing and not the other. When done, cut the tubing again to only 1/4 inch.
Take the throttle cable, and cut away the damage. This shortens the cable but does not affect the mechanism of the throttle. Put the new cable into the hole in the tubing, and then pull it out of the larger side. Fray the end so that it remains steady, and then pull it back enough so only the ends stick out of the copper tube.
Apply a large amount of flux to the tubing, and using pliers, solder the throttle at the copper end until the tube is full. Stop when the solder begins moving up the throttle cable. At this point, the repair is complete, so install the cable back into the engine.