Do I Have to Have Another Surgery to Remove Necrotic Skin or Will my Body Heal Itself?

Unfortunately, necrotic skin that is black usually means all layers of the skin are no longer alive, and almost always requires surgery to remove it. The dead skin has no blood flow, so it is also at high risk of getting infected. If there is concern that the tissue expander has also been exposed, it is definitely a good idea to remove it to prevent it from becoming infected and causing you to get very ill. 

It is difficult to say what caused the skin to necrose - skin sparing mastectomy in general is a great advance in breast cancer surgery, however it is very operator dependent, and very thin skin is at a high risk of having blood flow issues even with the slightest perturbation. It is hard to say if 300 ml of saline in the fill was too much, as it depends on how loose your skin originally was. 

Removal of dead tissue, especially in the presence of an implant or expander, is important and unfortunately does require surgical removal.  If there is partial thickness where the top layer peels off but the deep skin is pink (vascular) this may heal.  Turning black, as you have described it, would likely be the full thickness and would require removal.  Unless it would interfere with adjuvant (post-surgery) cancer treatment, you may want to consider your flap surgery sooner than later. 

The blood supply when performing a skin sparring mastectomy can always be of question.  If you have developed a full thickness wound and skin loss then there is the potential that the expander implant will become infected.  If Alloderm was used then there is a potential that things can be salvaged.  Your plastic surgeon is in the best position to understand your operation and give you the best advice moving forward.