Prepare the vegetables: Use a vegetable peeler to shave the carrot into long strips or ribbons. Do the same thing for the zucchini and yellow summer squash, rotating them as you peel so the ribbons stay about 1-inch thick. Stop creating ribbons once you reach the seeds. Add the ribbons to a medium serving bowl.
Prepare the beans: Open the can of cannellini beans and pour them into a fine mesh sieve and rinse under cold running water. Gently shake dry. Add to the bowl with the shaved vegetables.
Season: Add mint, vinegar, oil, salt, and pepper to the bowl. Gently toss to coat. Taste and adjust seasoning to your liking. Serve immediately.