There is no doubt that a general surgeon can remove the implants. But, generally speaking it is not just removing the implant, but also evaluation of the pocket for the capsule and abnormal fluid, etc. is also important. And plastic surgeons are usually more experienced at evaluation of the breast before, during and after explanation.
I would advise you to consult with a Board Certified Plastic Surgeon, certified by the American Society of Plastic Surgeons (ASPS) to discuss breast implant removal.