I did that in high school. I bought a $40 Stevens single shot 20 gauge and cut the barrel to 18.5" that was fun for a little while, then I cut the stock off into a pistol grip. I guess it was kind of neat, but not real fun to shoot. Have you ever fired a pistol grip 12 gauge? better hold on or the lever that opens the action will come back and draw blood from the web of your hand (Trust me, I know!) I think a super short double would be neat like the one in the movie "Gator" that Jerry Reed shoots but that's way under the legal limit and not really practical for anything besides hollywood. A .410 would be alot easier to use,but more expensive to shoot. I had a .410 contender and it was a hoot . My aunt gave me her old pistol grip .410 Mossberg pump and it's not bad at all. I never shot more than a box of shells through that 20 gauge after I cut the grip off and a couple years ago I traded it for a set of dies, and the new owner glued & pinned the rest of the stock back on (that I somehow hadn't lost/tossed/burned in 10 years) and mabe a useable truck gun out of it. My take on it:
sawed off barrel = fun
sawed off grip = pain.