Which of the following is a mechanical method of hemostasis?

Ligature is a mechanical method of hemostasis because it involves physically tying off blood vessels to prevent blood loss during surgery. This technique directly obstructs the flow of blood by constricting and securing the vessel, thus effectively controlling bleeding in a mechanical manner.

Other methods listed, such as laser and electrosurgery, utilize energy sources to achieve hemostasis through thermal effects, which can cause coagulation and tissue destruction. Although effective, these are not mechanical methods as they rely on heat rather than physical obstruction. Thrombin, on the other hand, is a chemical agent used to promote blood clotting, which also excludes it from being categorized as a mechanical approach. The use of ligature stands out as a straightforward, traditional method in surgical practice for achieving hemostasis through direct manipulation of the blood vessels.