Blend the chopped tomatoes in a blender until smooth.
Strain the tomato puree through a fine sieve to remove seeds and skin.
In a large pitcher, mix the strained tomato juice with vodka.
Add Worcestershire sauce, hot sauce, celery salt, black pepper, lemon juice, and lime juice.
Stir well to combine all ingredients.
Fill glasses with ice cubes.
Pour the Bloody Mary mixture over the ice.
Garnish with a celery stalk and a lemon wedge.
Serve immediately and enjoy your fresh Bloody Mary.