Does the US mint print two dollar bills with individual state designations?

No, because the Mint doesn't print any bills. They only make coins. Bills are printed by the Bureau of Engraving and Printing which is completely separate from the Mint.

Anyway, current $2 bills are Federal Reserve Notes like all other modern US currency. That means they're printed with seals indicating which of the 12 Federal Reserve districts requested them, the same as all other denominations. Federal Reserve Notes aren't printed for each state.