Why are people with poorly controlled diabetes more at risk for amputation?

Many reasons. Small arterial occlusive disease large vessel occlusive disease poor skin care easy infectivity (obesity and smoking are additional risks).
Several reasons. More likely to get neuropathy- can't feel it if they get minor sores, open skin, ulcers (must look at feet daily after take off shoes and socks) less able to fifht infection, so these injuries sores get infected have poor blood supply with blockages of arteries to fight so can't get white cells/ antibiotics to infected feet so infection spreads needs amputation.