Early cars used two pins, later, one spiral-cut pin.
First, get the punch out. You will have to get underneath and drive it upwards with a slightly smaller diameter of punch. Myself, I would take a punch of the same diameter and grind/file it top a smaller diameter. It is not going to be easy as I assume you have driven the stuck punch in hard.
Once you have the punch out, you need to use a pin punch of the correct diameter to prevent the same thing from happening again.