He got stabbed right in the damned heart.
Who Saved Him?
Ellsworth was the editor of National Publications (later DC Comics) in the 1940s, and by all accounts had one of the sissiest names in history. He didn't want Finger to kill off interesting villains (like he had done with Braless Woman and Sluterella in the past), so this time he told Finger to save the Joker. A new panel was quickly added.
Do all doctors react this way when they figure out a patient isn't dead?
If you want to know just how hard it is to think up good comic book villains, remember that scene played out in 1940. Hundreds of issues, a TV show and a bunch of movies later, he's still the best they could come up with.