From staff members at the Johns Hopkins Center for Gun Policy and Research (via The Washington Post):

Myth: Mental illness is behind most gun violence against others.

National opinion polls show that the majority of Americans believe that mental illness [sic]*, and the failure of the mental-health system to identify those at risk of dangerous behavior, is an important cause of gun violence.

Research says otherwise. Only an estimated 4 percent of violence against others is caused by the symptoms of serious mental illnesses such as schizophrenia and bipolar disorder. Impulsivity, anger, traumatic life events such as job loss or divorce, and problematic alcohol use are all stronger risk factors for gun violence . Research also shows that mental-health-care providers are poor predictors of which patients will go on to harm others. Further, most people with mental illness will never become violent, and most gun violence is not caused by mental illness.**

But mental illness is a strong risk factor for firearm suicide, which accounts for the majority of gun deaths in the United States. While improving America’s mental-health system would benefit millions of people with mental illness, it would not substantially reduce gun violence against others.

*I don’t support use of the terms ‘mental illness’ and ‘mentally ill’ as it implies acceptance of the biomedical model of mental health, i.e., that people who struggle with mental health issues are ‘sick’ and therefore need to be ‘cured’, typically through the use of pharmaceutical medications. This ‘Mental Health Literacy’ parable explains more.

**emphasis mine

(read the other myths here)