Place, cupped side down, on grate, cover grill, and grill until oysters begin to open, about 2 minutes.
Transfer opened oysters to a platter (discard any that do not open). Let cool slightly, then use an oyster knife or screwdriver to pry shells open, keeping cupped side down and retaining as much liquid as possible.
Using an oyster knife or paring knife, cut muscles connecting oysters to shells.
Serve warm with butter, lemon wedges, and hot sauce.