What practice involved draining blood as a supposed cure for illness?

The practice of draining blood as a supposed cure for illness is known as bloodletting. This historical method was based on the belief that removing blood could balance the body's humors, which were thought to cause sickness when out of balance. Bloodletting was commonly practiced from ancient times through the 19th century and was used to treat a wide range of ailments, from fevers to headaches.

The other practices listed do not involve draining blood for medicinal purposes. Burial rites refer to the customs and ceremonies associated with the disposal of the dead. Antisepsis is related to the prevention of sepsis and infection, focusing on sterilization techniques rather than blood removal. Exsanguination specifically refers to the process of draining blood, but it is typically used in a more modern and clinical context than traditional bloodletting. Thus, bloodletting is the most accurate description of the practice aimed at curing illness by removing blood.