If I exercise and skip doctor visits for all but injury and severe illness, will that save money?

Not in the long run. No one has a crystal ball with regard to health care costs for even known conditions that are stable. We certainly cannot predict what one will need over a lifetime. Preventive health care is very valuable and is something that doctors often include in annual exams or visits for illness. Having an experienced physician who knows one's personal, professional and medical history is, well, priceless.
Better ways 2 save $. 1) switch to generic drugs; 2) don't smoke & drink alcohol moderately 3) take advantage of wellness benefits; 4) take your medications regularly; 5) eat veggies; 6) pick a prescription drug plan wisely; 7) seek out bargains (for example, outpatient facilities often provide the same service cheaper than if consumed at a hospital); 8) choose the "right" doctor & follow his/her advice. Be well--
Hard to say. You are not giving much info in your question. If you have a medical problem such as diabetes, you may end up spending more money in the long run since you are not being cared for by a doc. Also, it is not clear if there are reasons why you may be risking injury without doctors care.