No - I had two removed and it doesn't hurt at the time. They numb the area first (obviously). I think they do that with an injection, which probably stings a bit (tbh I can't remember it so it can't have been bad!).
The mole-less area was a bit sore for a few days after, but no worse than if I'd grazed/cut the area. It helps to avoid wearing clothes that rub on the area.
Good luck!