Shot, even buckshot, wouldn't have much effect on a gun barrel. A 1-ounce soft lead 12ga. slug moving at 1500 feet-per-second might deflect one barrel, if it hit it just right, but that would only affect the accuracy of one round out of six per revolution. The most effective way to take a minigun out of action with a shotgun would be to shoot its operator. If the plot requires destroying the gun itself, you'd need something bigger, like a .50 Browning machine gun or sniper rifle that could smash the mechanism, or a rocket propelled grenade.