I'm having bad circulation in my legs and diabetes is causing my toe to become black. Will gangrene spread?

Depends. Gangrene is not like an infection that spreads on its own. It develops when tissue dies from poor circulation. The best way to check if the gangrene is going to progress is to evaluate the blood flow to the foot. This can be done with an arterial ultrasound.
See a specialist! These sorts of changes in any patient and in particular in the diabetic should be immediately evaluated by a foot specialist. Gangrene can not only worsen but can become infected and can rapidly progress to bone infection, sepsis and even death.
Yes. You need an endocrinologist to help maximize your diabetes care. You need a podiatrist to help with foot care. You also need a vascular surgeon or cardiologist, or interventional radiologist, like myself to treat your peripheral artery disease.