Relation between diabetes and foot amputation?

Vascular problems DM. Advanced diabetes leads to vascular issues that lead to tissue compromise starting at the distal extremities. When its bad enough, amputations start. The lesson is to control your diabetes as best possible and avoid any other risk factors for atherosclerosis.
At risk. Statistically diabetic have an overall higher probability of developing gangrene and foot infections that will result in amputation as compared to those who do not have diabetes.
Yes. Diabetes destroys the peripheral circulation. Faster when out of control, slower with good control. The feet as the most distant part of the circulation are the most vulnerable. Good news, the Insulin pumps just keep getting better. If you don't have one yet, you may in the near future.