Once those wires get cut there basically dead, but if your right next to the truck then it should still work. It sounds like the receiver batteries are dead in the car, and or the remote. Its a good idea for a first car to get a fail-safe, a fail-safe in the event of loss radio signal or low battery will apply the brakes and not allow the car to take off and cause a run away.
This will be the best money you will spend on that car, as it will protect it from taking off at wot (Wide open throttle) into someone, car, woods, etx...
http://www3.towerhobbies.com/cgi-bin...&I=LXHLV3&P=ML