People with mental illness are not violent. Knowing the mental health status of someone gives you very little predictive power about whether they pose a risk of violence or not - even if we restrict ourselves to severe illness such as psychosis.

Even if you were to find that every single terrorist has a mental illness (and we know that most of the killers in the UK didn't) it still gives you no useful information.

Violence is prevalent. Mental illness is prevalent. There's obviously going to be some overlap. It's a coincidence, not a cause.