Typically, surgeons have to make incisions that are relatively big during surgery, whereas the small instruments of a robot can fit through smaller incisions. Given this advantage of robotic systems, it’s now quite common for surgeons to use remote-controlled robotic arms to perform surgery—combining the precision of an experienced human with the minimal invasiveness of a small robotic arm. Nevertheless, the surgeon is controlling the robot in these cases, and a fully automated robotic system that can outperform surgeons in terms of precision is yet to be realized.

A recent advance shows that robots could surpass human performance in the near future, however. In a paper published 10 May in IEEE Transactions on Automation Science and Engineering, a multinational team of researchers reported the results of a study where a robot was able to complete a common surgery training task with the same accuracy as an experienced surgeon, while completing the task more quickly and consistently...

Using one arm, the surgeon outperformed the automated robot in terms of speed. But in the more complex tasks involving two arms, the robot outperformed the surgeon.

For example, for the most difficult task (bilateral handovers), the surgeon achieved a success rate of 100 percent with a mean transfer time of 7.9 seconds. The robot had the same success rate, but with a mean transfer time of just 6.0 seconds.

“We were very surprised by the robot’s speed and accuracy, as it is very hard to surpass the skill of a trained human surgeon,” says Ken Goldberg, a professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley, who was also involved in the study. “We were also surprised by how consistent the robot was; it transferred 120 blocks flawlessly without a single failure.”

(Via IEEE Spectrum)

As far as I know, one of the earliest references (and illustrations) of the phrase "robot surgery" occurs in Secret of the Buried City, by John Russell Fearn and published by Amazing Stories in 1939:

His nostrils drew in the sweetish, sickly odor of powerful antiseptics..

Wearily he opened his eyes, lay gazing in blank wonderment at a shadowless flood of light contrived from somewhere in a metal ceiling above him. His first impression, which he just as quickly dispelled, was that he was in some kind of hospital. But the instruments around him were ahead of those in any hospital, despite the advanced surgery of this year 1967. Further, the objects moving about so gently and putting their instruments away were not living beings, but robots. Three of them — perfectly fashioned creatures of metal, even with strong resemblance to human beings in outline and face, but just the same still mechanical.

(Robot Surgery from 'Secret of the Buried City' by Fearns)
"Robot surgeons operated on Rodney Marlowe's
injured head with superhuman efficiency."

(Read more about robot surgery)