Why Won't Dermatologists Remove the Mole Completely?

I can't speak specifically to your case. It may be in cosmetically sensitive area, and the doctor wants to decrease the risk of unacceptable scarring. Whenever possible, when performing a biopsy on a suspicious pigmented lesion the entire lesion should be removed. If the lesion is particularly large or removal of the entire lesion might leave an unacceptable scar, biopsy of a portion of the pigmented lesion (e.g. the darkest or most raised portion) is recommended. Best to discuss your  situation with your doctor with these considerations in mind. Good luck.

Your plan of removing the mole completely and send it for biobsy, is much logical. Since if there is any thing to be concerned about then the pathologist has a better chance of proper diagnosis and in case of melanomas to stage the tumor. Shaving will not do that.

The good news is that when a mole is removed using a shave biopsy technique, it is actually "shaved off" at a level just below the surface of the skin. This method is quite effective to remove moles and leaves a minimal scar. The procedure typically takes less than a minute, and is fairly painless. Only if the biopsy reveals the mole to be precancerous is further surgery required. Moles that are removed in this fashion will rarely recur enough to be bothersome. I would recommend having this treatment done by a board certified dermatologist, as plastic surgeons rarely do shave excisions as you can see from the answers below.