Unwrap the corned beef and pat dry with paper towels. Allow the beef to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for indirect cooking over medium heat (350° to 450°F).
Arrange the celery, carrot, onion, and garlic in a 9-by-13-inch heavy-duty foil pan. Place the corned beef on top of the vegetables. Sprinkle the contents of the spice packet over the corned beef and rub into the surface of the meat. Add the tomatoes; fill the empty tomato can with water and add to the pan. Cut the tomatoes into 1-inch chunks.
Brush the cooking grates clean. Tightly cover the pan with heavy-duty aluminum foil and grill over indirect medium heat, with the lid closed, for about 2 hours. Remove the pan from the grill. Add the cabbage wedges and potatoes around the corned beef and spoon the cooking juices on top. Cover the pan with foil and continue grilling over indirect medium heat, with the lid closed, until the corned beef, potatoes, and cabbage are tender, about 1 hour more. Transfer the corned beef to a cutting board and spread the mustard on top. Let stand 5 minutes before carving the meat across the grain into ½-inch slices. Serve corned beef slices with the cabbage and potatoes, with juices spooned over all, along with grilled rye bread, if desired.