That opening "get me my gun" verse colors the rest of the song and adds a somewhat ominous tone to otherwise innocuous lyrics such as:Go down by the river, babe
Honey, I will meet you there
Go down to the river, babe
Honey, I will pay your fare
Other than that bit about the firearm, though, the song seems to be pretty straightforward and nothing more than its title sells - a guy is trying to get his woman to stop crying. By the end of the song, he seems to have gotten his worst emotions under control, wrapping things up with the plea, "So baby, please stop crying 'cause its tearing up my mind."
David Weir at Bob Dylan Song Analysis
makes an interesting observation that the "bad man" may also be the narrator himself, speaking in third person as people sometimes do after they've done something terrible or something while intoxicated. A "that man wasn't me" sort of thing. There's no way to be sure this is what was meant, of course, but it does add an intriguing element to the song.