Normally, you will go nowhere, it will be another sea day. If that does happen, they will credit your port taxes. Mahogany Bay is difficult to get into under ideal circumstances, but it is a great port. Coxen Hole is the other port they use there. The first time we went, there was no Mahogany Bay. We tendered in as the pier would only accommodate one ship. It might be possible that they would tender, but not probable. If it's too rough to get into Mahogany Bay, it would be too dangerous for tenders, more than likely.
We did an excellent snorkeling excursion through Carnival when we went to Belize. They took us to the reef for a fabulous snorkel, then to a private island. It was well worth the money. The snorkeling boat picked us up from the ship and returned us to the ship. The private island was fantastic, nice beach area, chairs and shade with a small shop. To get into Belize itself, you will need to take a tender from your ship. The ride is 15-20 minutes and the tenders run nonstop while you're in port. Just be sure not to miss the last tender!