A 2015 study pitting the ~50 autonomous cars in California against the nationwide statistics for conventional cars found the accident rate of autonomous cars to be about five times that of the national average, with four times the injury rate.
However, the study also notes the very small statistical base -- there were just 11 accidents on file for autonomous cars in 1.2 million miles. It also notes that the accidents were mostly at slow speeds with minor injuries.
Google claims that in none of the mentioned cases, the autonomously driving car was at fault.
A more recent article mentions other numbers. A federal inquiry to a deadly crash involving Tesla's autopilot found that Teslas with autopilot are crashing 40% less frequently than Teslas without autopilot.
All this is somewhat inconclusive as to whether today's self-driving cars are already safer than human-controlled vehicles. But that is not actually the claim here, is it?
Claim vs. Interpretation
You write that you interpret the claim to mean "that a self-driving car has a higher mileage per death than human driven cars."
But that is not the claim, is it? The claim is that hundreds of lives could be saved if all cars were self-driving. That is a hypothesis, really, and does not have to be backed by any current self-driving-cars-in-human-controlled-traffic numbers. It is about what would happen if the human factor were eliminated (as far as other cars are concerned, of course you still have pedestrians and cyclists etc.)
The wired.com article linked in the first section of this answer mentions that 40% of fatal car crashes in the US are the result of drunk driving, and 16% the result of distracted drivers. It also notes that as many as six million US drivers admitted to having hit another car on purpose. How many of these accidents would be avoided if all cars were self-driving?