It looks like “spud guns” are exempt for this definition, as are mortars & “bazookas”.
"designed to expel a solid projectile or projectiles by the action of an explosive or a burning gas"
I wouldn't push that "spud gun" thing too far as potatos are "solid projectiles" propelled by a "burning gas". You could try those 20oz. soda bottles and squeeze by under a technicality.
It looks like mortars and bazookas might sneak by because the projectiles are explosive not solid.
That would seem to give a pass to any sort of artillery firing explosive rounds. Federal (BATF) rules, however limit rifled bore size to .500" or less. Anything larger is a "destructive device" and requires an ATF Form 4 w/ a $200.00 excise tax stamp.
Smooth bores are OK and as long as you stay away from "solid shot" you can build yourself a cannon (the fastest way to convert black powder into fun!).