Can a general practice doctor perform liposuction?

In the US, a license to practice medicine allows a doctor to LEGALLY perform any treatment they like (brain surgery, leg amputation, allergy shots, C-section, or manage blood pressure).  
The question you should be asking yourself is, would you ask your general doctor to perform a hip replacement for you, even though they are legally allowed?Your health and safety matter.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 
I hope the answer is obvious.  Just because it's cosmetic, it doesn't mean it's not real surgery.If you can't afford a properly trained safe surgeon, save the money you have (and your health), and avoid surgery altogether.

Liposuction remains the most popular plastic surgery procedure performed across the country.  It is extremely safe, relatively painless, and offers quick recovery.  However, disasters have been reported.  I urge you to seek a board-certified plastic surgeon by the American Board of Plastic Surgery, which is the only board recognized by the AMA for plastic surgery on the head, neck and breasts and the entire body.  Another credential worth investigating is if the surgeon is a member of the American Society for Aesthetic Plastic Surgery.  This assures you that this surgeon is board-certified and has the expertise in aesthetic surgery.  Do your research.  I often find patients spend more time researching a pair of shoes than they do a surgeon for this type of procedure.  

Yes, it may be possible, but for best results I recommend seeing someone who specializes in high definition physique procedures. For best results, I recommend a hi definition procedure like VASER liposuction. I use VASER HI DEF with ThermRF and fat grafting to get the most fat removal, skin tightening, contour and definition. This combination will give you the most toned result. I recommend getting a formal evaluation with a hi definition physique expert. Best, Dr. Emer