Combine carrots, potatoes, onions, celery, green beans, corn, peas, Worcestershire sauce, Old Bay, mustard, red pepper flakes, and 6 cups water in a large pot. Add tomatoes, crushing them in your hand, and juice from can. Bring to a boil over medium-high heat, then reduce heat to medium-low and simmer for 30 minutes.
Add crabmeat to soup and simmer 35 minutes more, stirring often. Season to taste with salt and pepper.