You can think of it as a way to emphasize an action, most often used when referring to anything dealing with speech (or snoring!) . "Snoring his head off" = "Snoring very very loudly". If I wanted to say that my friend kept talking and talking and talking, even though I wanted him to stop, I could say "Oh wow, Billy really talked my head off yesterday."

I don't know if there is a similar expression in Spanish, but it might be something like: Está roncando con tanta fuerza que pueda decapitarse (a sí mismo), o algo así.