In a large blender or food processor, combine the sweet corn, cucumber, red bell pepper, red onion, tomato juice, lime juice, cumin, salt, and black pepper. Blend until smooth.
Taste and adjust seasoning if necessary, adding more salt or lime juice to your preference.
Stir in the chopped cilantro and pulse a few times to combine, leaving some texture in the soup.
Transfer the gazpacho to a large bowl or container and refrigerate for at least 2 hours to chill and allow the flavors to meld.
Serve the gazpacho in bowls, garnished with diced avocado and extra lime wedges on the side.