it has to kill the alternator and the battery, along with the rest of the electrical system. Mine still doesn't technically work right. The alternator feed wire runs to the fuse box and to the battery (on my 66 anyway), I only isolated the alternator feed wire running to the battery. Needless to say, the kill switch doesn't kill much. I later wired up a relay to the kill switch, feeding the ignition, so now when I flip the switch it disables the ignition and the battery, but not the entire electrical system (because the fuse box can still draw power from the alternator when the engine is running). This is not NHRA legal. I need to get in there and redo all the alternator wiring so it will be legal. In other words, it can be a pain.
But anyway, a few basic rules. NHRA requires the positive be switched (thats what makes it complicated). If you use the kill switch to break the ground, you will not pass tech, even though the switch will effectively kill the electrical system. You'll run the battery+ into the switch, and a +cable from the switch to the solenoid, where the car will draw power. The main feed from the alternator must go to the +battery side of the switch. As a aside benefit, the battery will be able to absorb any voltage spikes, so it creates a more stable system, if you will. If it is wired to the other side of the switch, the alternator will continue to feed power to the car when the switch is flipped.