If i ask to have my mole removed under general anesthetic will they allow it?

Perhaps: It would depend on the size and location of the mole, your health status, and the recommendation of your surgeon. Children routinely have procedures like this done under general anesthesia, but for a simple mole on an adult, a local anesthetic is usually sufficient.

Anesthesia for skin: Moles are generally removed with local anesthesia. Some needle-phobic patients request sedation or general anesthesia. Find a physician you can communicate with and trust and you will probably find your mole removal to be virtually painless.