General anesthesia for facial fat transfer?

Hi Iluvelvi,
Unless you're also having large volume liposuction or other concurrent procedures, general anesthesia typically is not required, even if the fat is being removed from a couple different areas.  That being said, it sounds like your surgeon feels more comfortable doing your procedure under general anesthesia.  It is important that you and your surgeon are on the same page before undergoing your procedure.
Best wishes,
Dr. Jay

Fat grafting can be performed under tumescent anesthesia without the need for GA.  Although  GA is an acceptable  technique, it is  not required unless there are very specific issues that are not evident in your question.  Once the tumescent anesthesia is administered, most patients are very comfortable for the amount of lipoharvest  you discussed.  Small amounts of local anesthesia are then placed In the face (nerve blocks), and the grafting is completed. 

Facial fat grafting is routinely done under local anesthesia. General anesthesia is also an acceptable alternative depending on the patient. Harvesting 60cc of usable fat under local is not a challenge. Surgeons perform liposuction upto 4 litres under tumsecent anesthesia.
I would suggest you visit a plastic surgeon well versed in using local anesthesia techniques