If your new car's door is badly damaged how do you get the insurance company to replace it with a new door instead of just repairing it?

Depends on how it was damaged. If it was another drivers fault, take it up with their insurance company, by getting estimates of a new door and submitting it to them. If it damaged the vehicle bad enough, by making it unsafe to drive or bending the frame, it would be safer to replace it anyways, rather than repairing it.