The following is a Christian perspective, with some parallels across the religious spectrum.
Mental illness is not caused by demon possession. It can sometimes seem like other powers are in control or impacting a loved one and the causes of mental illness are often not clearly traceable or understandable. But there is simply no evidence of mental illness being caused by demon possession. The same thing used to be said for all kinds of other illnesses, diagnoses that none of us would give today. One of the ways that citing mental illness as demon possession further wounds a person with mental illness and his or her family and friends is that the next step is often claiming that a lack of healing is a lack of faith on the part of the person or, sometimes even worse, on the part of the family. Anyone who asserts that must realize that if they could not cure someone by faith (of any disease or especially mental illness), that is also a judgment they have to make against themselves. Rather, individuals and families need the faithfulness of friends, extended family, professionals, and faith communities who can walk with them, support them, and prevent the kind of isolation and stigmatization that often accompanies mental illness.
Links to the resources below are provided by Bill Gaventa, a foremost US advocate and leader in inclusion of people with disabilities. They are Christian in orientation.
http://www.mentalhealthministries.net/ Mental Health Ministries
www.pathways2promise.org<http://www.pathways2promise.org> Pathways To Promise