To throw out another number for comparison, medicare and medicaid together cost about $50B / year in the state.
The Tampa Bay investigation's violence refers to violence in the hospitals itself and not the general violence in society. For 13.5K per year you might reduce the hospital staff by 10% but that is unlikely to result into chaos that the report seems to suggest.
By the way, for comparison, Medicare spends $10k/year per beneficiary in Florida.
Your math only works if mentally ill people receive no other services from the state whatsoever. Assuming the mental hospitals receive supplies by road, this is not true.
To put this in perspective, Florida spent over $2.2B on its corrections system in 2014 [2].
[1] http://www.fpi.institute/floridas-provision-of-mental-health...
Based on...?
Of course there is a whole point of whether government ought to spend some money now to avoid spending on basic services later whether there are proper studies done and if people agree to it and if the mental hospitals are free for everyone. But that was not my question here.