Don't let the mention of ARs in the previous post confuse you.
you CANNOT legally cut the barrel on any rifle shorter than 16" without NFA paperwork (ATF form 1).
You CAN assemble a new firearm from a virgin receiver as a pistol with a barrel shorter than 16". If a receiver has been used to make a rifle, merely removing the stock and barrel are not sufficient. If it is assembled as a rifle it is a rifle legally and you can't make a pistol from it.
Stopping power: The power some guns have to make you stop what you are doing and get your wallet out.