I wanted to show that you can cut down or "saw-off" a shotgun without making an ugly hack job of it. When a long gun bursts it isn't always necessary to replace the barrel or discard the gun. In this video I go through the process of repairing a 12ga hunting shotgun with a barrel split due to obstruction. The gun is now 8 inches shorter and lacking any choke so it isn't much use for birds beyond 20yds or so but it is still usable. Yes this makes it a "sawed-off" shotgun but that doesn't mean it is illegal. This gun remains 4 inches over minimum barrel length and way over minimum gun length so it is legal by federal standards and the standards of the state of Montana. You need to research the laws where you live and follow those.
Safety: I can't stress this enough, have the gun inspected after your work BEFORE you shoot it again by a reputable and licensed gunsmith. Be honest with them as to how it broke (if you know) and how you fixed it. Ask them if your work is sound and the gun is usable.
Disclaimer: guns are inherently dangerous, modified guns even more so. Yes you can "saw off" a shotgun but this is a much cleaner and more professional job. Make sure you remove all ridges from inside the barrel or it will simply burst again...only closer to your face.
Legal stuff: I do not know the gun laws where you live It is your responsibility to know and follow them. I do know that shotguns barrels measured from the head of the shell when loaded MUST be longer than 18 inches or it is a serious crime. Additionally the overall length must be at least 27inches. Their are variations of this and permits/licenses you can get but these are the rules, as I understand them. The ATF has very little sense of humor.