What kind of doctor performs a circumcision?

Several. It can be done by the ob, the baby's pediatrician or a local surgeon or urologist.
Many. Obstetricians, urologists, pediatric & general surgeons, some pediatricians and family or general practitioners circumcise infants. Non surgeons have to pay higher malpractice premiums and thus do not do them. Children of all ages are cir'd by urologists or pediatric surgeons. Adults are best circumcised by urologists.
Depends. Depends where you are. In some locales, the pediatricians do them, while in others the ob's do them. Depends on who has kept their training up. I, for instance, haven't done one for 12 years, so it wouldn't be me, but the ob's are happy to do them. A few family practice docs will do them, especially the "old time ones", and ones in rural areas, .