A man who operates on sick people

One word substitute is Surgeon.

Physician: a person qualified to practise medicine, especially one who specializes in diagnosis and medical treatment as distinct from surgery.
Operator: a person who operates equipment or a machine.
Surgeon: a medical practitioner qualified to practise surgery.
Physiotherapist: a person qualified to treat disease, injury, or deformity by physical methods such as massage, heat treatment, and exercise.