Heat olive oil in a large saucepan over medium-high heat. Saute celery, onion, and garlic until onion is translucent, about 5 minutes. Pour mixture over the ham bone in the slow cooker.
Saute carrots, potatoes, and red bell pepper in the same saucepan until coated in oil, about 1 minute. Transfer vegetables to the slow cooker; add water, black beans, vegetable juice, corn, tomatoes, green chiles, cumin, salt, and black pepper. Cover and cook on High until soup is warm, 45 minutes to 1 hour. Reduce heat to Low; continue to cook for 5 to 6 hours.
Remove ham bone from the soup. Separate meat from the bone and return to the soup; discard the bone. Cover soup and refrigerate, 8 hours to overnight. Discard thick fat on the top of the soup and reheat.