In a blender, combine the vegetable juice, lime juice, 1 celery stalk, hot pepper sauce, Worcestershire sauce, horseradish, vodka, and crushed ice. Season with salt and pepper. Cover, and blend until smooth.
Use two large frozen beer mugs, highball or pint glasses. Place one cocktail onion at the bottom of each glass. Put 1/2 cup of ice cubes into each glass. Use a vegetable peeler to pull a few strips off of the carrot for each glass. Put in a slice of green pepper. Divide the blended mixture evenly between the two glasses.
On cocktail toothpicks, place a green olive, a cocktail onion, and a lime wedge. Attach each one to a celery stalk so that when inserted, this garnish is on the top of the drink. Sprinkle on a few more carrot strips, and garnish each drink with a sprig of mint.
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