It is all about weighing percentages. More mental health access can reduce the numbers.
That aside, this whole mental health thing is a tangent. The point of the OP is that these crimes are a negative externality of gun and bullet ownership so to correct for a market shortcoming in pricing, it should be taxed. Think of it as analogous to carbon emissions- right now a company does not properly factor in the cost of the pollution into its prices because the cost is shared by the entire world- not just it- that pretty much makes it negligible for the company considering the size of the Earth. A Pigouvian tax on carbon emissions would by put in place to internalize that cost to the company. Same issue here with the bullets.
Economically, a valid counterargument might be that there is a greater positive externality of gun and bullet ownership that offsets the negative externality in and of itself. But no one has made that argument yet. Instead, the focus of this discussion has been on the use of the tax money, which wasn't really my point in the first place. But that is fine- interesting discussion nonetheless.
Okay...accepted.