Mental disorders and violence are connected, but not in the way most people think. It is now outdated to regard "crazies," "sickos" and "weirdos" as being automatically dangerous or threatening. With our improved understanding of mental illness and associated disorders, we know that mentally ill people are often docile and harmless and, even when they act out, lack the behavioral organization needed to commit purposeful violence. Yet mental disorder in the sense of temporary or chronic mental disturbance is strongly associated with violence in ways unrelated to mental illness. Some would even say that every person who commits violence has a temporary or long-lasting mental disorder.
Statistics establish that a mentally ill person is one hundred times more likely to be the victim of a crime than to commit one. This is also true of violent crimes. While the news media sensationalize every case of a schizophrenic who is shot dead by police for waving a knife around, such cases are extremely rare. Most mentally ill people are wrapped up in their own problems and unable to interact with the outside world effectively. Even when they decide to do someone else harm, they are often unable to organize their own behavior enough to even come close to succeeding. The homeless man you see walking down the street mumbling to himself or even shouting at invisible people is perfectly harmless. Far from seeking to hurt you, he probably doesn't even notice you. It is still wise for laypersons to avoid such people, but there is no reason to be afraid of them.
Most violence, however, does have psychopathological roots. Some violence is caused by temporary disturbances in mental function, such as the well-known "crimes of passion" where someone is overwhelmed by their own emotions and commits violence. Other people have chronic disorders ranging from personality disturbances to abuse survivorship, and commit violence from motivations that don't exist among the nonviolent. At the extreme are what used to be called sociopaths and psychopaths, whose identity is centered on their opposition to the dominant social order, and who use violence against others as a way of defining themselves. While some experts say that all of these categories of violent people suffer from mental illness, other experts make a sharp distinction between someone who is ill and needs treatment and someone who is just plain nasty and needs to be kept away from potential victims.
With advances in the understanding of mental function over the past twenty or thirty years, experts have learned to be less crude in their classification of mental disturbance. Thus there is now more acceptance of the gentle, harmless mental patient who needs treatment, and a harsher attitude towards the often incurable social deviant for whom violence is a structural mental necessity. Put simply, there are at least two types of mental disorder, among those who are sick and among those who are evil, and it is almost exclusively the latter who are responsible for violence. They still suffer from mental disturbance, but one far different from mental illness.