Surgical instruments have hardly changed since ancient times, though standards of asepsis and anaesthesia have much advanced.
As today, a sharp knife (scalpel) was used on soft tissue. A bone-saw was used where necessary. Needles and catgut were used to sew up the wound, and severed arteries were bound up with silken or gut threads. A surgeon of the 19thC would not be totally lost in a modern operation.