Before the 19th century operations were horrific procedures, and most patients died from post-operative shock, infection, or loss of blood. In some London hospitals the death rate after operations was over 80 per cent.
The 19th-century up-turn in surgery actually pre-dated anaesthetics and antiseptics. Many new ideas were trialled in America (eg Dr Thomas McDowell performed an ovariotomy in 1809), with some success. One suggestion is that American surgeons were happier to try out new techniques on Black slaves.
The improvements in anaesthetics (to protect patients from pain) and antiseptics (to protect patients from infection) occurred because surgery without them was too traumatic, and patients couldn't survive it. New blood transfusion techniques also saved many lives.
The number of operations grew hugely through the century, and surgeons became skilled at internal operations (1880s: first appendectomy; 1896: first open-heart surgery) and even tried (unsuccessfully) to transplant organs such as thyroid glands and testicles. Various factors pushed the process along: