From Greek 'cheirourgía' (hand-work), combining 'cheír' (hand) and 'érgon' (work) — surgery is literally 'working with the hands', distinguishing it from medicine of the mind. English uniquely dropped the 'ch-' that French, German, and Spanish all kept.
The branch of medicine concerned with treating injuries, diseases, and deformities by manual or instrumental operations on the body.
From Old French surgerie (a contraction of cirurgerie), from Latin chirurgia, from Greek cheirourgía (hand-work, craft done with the hands, manual operation on the body), a compound of cheír (hand) from PIE *ǵʰes- (hand) and érgon (work, deed) from PIE *wérǵ- (to do, to work). Surgery is literally hand-work — the branch of medicine defined by manual intervention rather than the administration of drugs or diet. This reflects the ancient Greek distinction between two kinds of medical knowledge: the physician (iatros) who prescribed treatments from knowledge, and the cheirourgós who operated with tools and hands. Greek érgon gave English energy
English is almost alone in dropping the 'ch-' from the Greek root. French, German, Spanish, and Italian all preserve 'chirurg-'. The English word was mangled through Old French dialectal forms where the initial 'ch' became 's', giving us 'surgery' instead of the expected 'chirurgery' — which did exist in English until the 18th century.