Running over a snake will not kill it, at least the rattlers we have in Colorado. One needs to hit the brakes as you run over the snake to lock the wheels. That does the job!
I ran a rattler out of my yard with a garden hose. Turns out they dont like to be wet. I didn’t have snake shot at the time. That problem has now been solved....
Yes I know about the hitting the brake trick, I have used it myself on south Texas rattlers. It peels them out of their skin!