A circular tool with a blade is pressed into the skin around the mole to cut it out. Since the cut usually goes pretty deep, your doctor will then put in a few stitches. Which mole removal method ...
In the past, I've had a couple of moles cut out but that was because they rubbed on my clothes, not because they were suspicious. I would rather be out mountain biking or waterskiing than sunbthing.
Red moles, known as cherry angiomas ... so they ask their healthcare provider to cut off the lesions. However, they're not dangerous, so there's no medical reason to remove them.