We already limit guns from the mentally ill. Further laws are not going to work.
The problem is people have guns. What is keeping the armed teacher from killing a student or co-worker? What is keeping the co-worker with a gun from taking it to work? What is keeping the police officer from shooting an innocent person? What is keeping people from shooting an ex, a child, or a parent?
The answer isn't more complicated laws. The answer is to eliminate guns outright - not just certain types. There is no reason for owning a gun aside from hunting. I don't care if you think you need one to protect yourself - the only reason you do that is to protect yourselves from other people with guns. With no guns, we eliminate not only mass-murders but the daily murders we deal with all the time