In a blender, combine the tomato juice, lime juice, lemon juice, cilantro, jalapeno, horseradish, and garlic and blend until smooth. Season the mixture, to taste, with the Worcestershire, salt and pepper. Store the mixture in a nonreactive container. Refrigerate the mixture for at least 6 hours and up to 3 days before serving.
To serve, fill 6 large (16-ounce) tumblers with ice, divide the Bloody Mary mix among the glasses, and divide the vodka evenly among the glasses. Garnish with the sliced lime and celery stalks and serve.