But you do agree that mental institutions and jails are needed. Unless you want to have the mentally ill "contract" to pay for their care and the victims of crime forced to pay again for the jail, you need tax.
The mentally ill aren't violent are they? If they are, then there are a number of options available to the victims. Again, taxing isn't necessary here. You could join an association of jail service providers, and pay membership fees, etc.
I know it sounds unusual, perhaps even a bit unorthodox, but you never know, it might just work. Just because there isn't anybody trying it, doesn't mean it won't.