meaning - What the expression "I drive the hearse" means?

To begin with, this is a terribly tortured song. The songwriter is conveying his raw emotions in very veiled writing, using metaphor after metaphor to the point that it is an exercise in literary analysis much like what takes place in a literature class. Even an experienced native speaker would have a hard time figuring out exactly what the songwriter is saying (although the gloomy mood is quite clear).

Freedom cannot actually stain a coat, and you can be sure that the narrator doesn't go out in the garden and make holes in the ground ("I dig the dirt"), but this may be a reference to digging a grave. Since on a literal level, driving a hearse means transporting a dead body, clearly the narrator is conveying a negative message about his actions when he falls (although what that means isn't exactly clear, either).

Much of this song is metaphorical, and with so much metaphor, it's impossible to know what's really going on. We just know that the narrator is feeling hopeless.

Also note that at this website there is a discussion of this song.

Short answer: Driving a hearse is not a typical idiom. In this song, it means whatever the author is using it to mean.