In a large Dutch oven, pour the oil to a depth of 3 inches; heat the oil until a thermometer reads 350 degrees F.
In a shallow dish, combine the flour, cornstarch, dill, salt and mustard.
In a separate shallow dish, pour in the buttermilk. Dredge the grouper strips in the flour mixture. Dip in the buttermilk, and dredge in the flour mixture again to coat.
Fry the grouper fingers, in batches, until golden brown, 4 to 5 minutes. Drain on some paper towels. Serve immediately with the Yummy Sauce.
In a small bowl, combine the mayonnaise, onions, relish and dill. Season with lemon juice, salt and pepper. Cover and chill.