Do you typically have to pay tax on a food stamp purchase if you utilize a store or manufacturer coupon?

It is not a "food stamp purchase". It is partially a food stamp purchase, and partially a coupon purchase. For sales tax purposes, coupons are like money. The tax is the same as if you used however much food stamps you used and $2 of actual money. In other words, there is no tax on what you got with the food stamps, but there is tax on what you got with the coupon, the same amount of tax as if you used $2 of actual money to buy something.