The last person to be tried by court martial, sentenced to death, and actually executed in the Armed Forces for a "military" crime; was Private Eddie Slovik in 1945. He was accused of desertion for running away during the Battle of the Bulge.
There have been servicemen sentenced to death, and perhaps a few executed, for "non-military" crimes such as murder or rape.

Gotta love auto-correct.

Dissertation? Does that means he's getting a Ph.D.?
http://redkincaid.com

Before a court martial there would likely be one or more hearings to determine if a court martial is warranted. In this case,it would probably be decided to not have a court martial. For comparison look at what is currently happening with Beau Bergdahl (if I spelled that right). He's the army sergeant awaiting court martial for dissertation.

Great explanation, thanks. Going back to the episode though, in the 1960's (or 70's as the writers would have us believe ) would Capt Crane have been court martial le for mutiny, even though he saved the ship? He did draw a gun

No, but mutiny is forcefully removing the CO and anyone who supports him, from command, and taking over the ship for whatever purpose. In civilian speak it's like a bunch of police officers throwing the chief of police and his friends on the force in jail.
How do you punish that? For the military it's usually with death because these people are supposed to be killing the enemy, not taking over your assets.

Thank you, Blueghost. Not a pleasant thought

Technically it probably is, but any death sentence in the modern navy (unless during wartime, and specifically during a battle) would take place after a court martial on shore. And the death sentence might be lethal injection or gas chamber.