You can look at all the data in the last 50 years and it categorically points to those afflicted with actual, diagnosed mental illness (e.g. schizophrenia, clinical depression, autism, etc) are much more likely to BE the victims of violence. Not the cause.
Almost all of the cases I can think of from recent memory (outside of Gifford's shooter) were actually uneducated, misguided, angry a**holes.
It's a lot easier for everyone to swallow if they are labeled "mentally ill" instead of realizing the actual root cause of why these individuals do what they did.
Conveniently, it also allows society to distance themselves from the actions as opposed to realizing some of the some thoughts/beliefs they may share with the individuals.