Perfectly legal to cut a barrel. So long as you do not have possession of a firearm that it fits. If you shorten a rifle to less than 16" (26 overall) or a shotgun to less than 18" (26 overall) you are "building" an NFA firearm, and must get approval to build a SBR or SBS, and pay the $200 tax. Same law that regulates full autos, suppressors, and artillery.
If you possess a Mossberg 500, AND a second barrel for a 500 cut below minimum length, that is considered "constructive possession".
Penalty for possession of an unregistered SBS or SBR is 10 yrs in a Federal prison and a $10,000 fine. So yes, you need some paperwork to do that.