Does a restaurant have to pay tax on a discount?

In almost any jurisdiction, the restaurant will pay tax on the amount after the discount.

Discounting is just a selective way to reduce prices for particular clients and thus achieve some degree of price discrimination. It's no different in principle to cutting prices for everyone or having a sale or similar.

It would be very strange for a tax jurisdiction to work any other way, because businesses would end up being taxed on money they never actually got. While tax systems often have that kind of anomaly in rare cases at the edge of the system, discounting via vouchers is extremely common. For example, here are the rules in the UK.

I owned a restaurant for over 5 years.

Sales tax was only collected on POST discount price, though every state that collects sales tax may have different laws regarding collection.

For example, when a customer used a gift certificate, that did NOT reduce the amount that tax was collected on. Why? Because the restaurant at some point or another collected the full amount of the bill.