It’s really the guns though that sets Americans apart, not the mentally ill. You can concentrate on massacres but when looking at total gun deaths the majority are just single murders.
Australia has recently had two massacres where a male has shot and killed family members and killed himself. One man went through the drama of joining a pistol shooting club to obtain the license and revolver he used to shoot his family.
I’ve know people who have given up all their firearms when going through divorce or other rough times, scared they might turn one on themselves. In the USA it’s very easy to obtain guns, they are extremely popular so with gun ownership so high they will always have more gun deaths.
Mental health and gun related deaths are largely separate issues, seems inevitably disastrous though when guns are so accessible even for the legitimately insane.