In the U.S. the correct spelling is "sawed off." It refers to a shotgun whose barrel has been "cut down" with a saw to shorten the barrel and the effective range. In Britain a sod off shotgun is a shotgun used to tell a bloke to "Sod off!" Different type of gun entirely.
I'm picturing it as a movie that's a combination of Saw and Shaun of the Dead--I can see Shaun at his favorite pub, the Winchester, where he has to tell Jigsaw's victims to sod off because it's his turn to play pub games. Ooh! We could call him Sawn of the Dead.
Thanks Matthew. Where I'm from, sawed-off shotguns, as we call them, are illegal. I meant sod off shotgun as a false analogy to "sod off", an infelicitous and vulgar way to tell someone to go away. With a shotgun.