Combine the garlic, chickpeas, beet, tahini, 2 tablespoons lemon juice, water, salt, and cumin in a food processor and puree until smooth. Taste for seasoning.
In a separate bowl, combine the yogurt and remaining lemon juice. Whisk until smooth and season to taste with salt.
Transfer to a serving bowl and garnish with the lemony yogurt, a drizzle of olive oil, the mint leaves and some reserved chickpeas and beets. Serve alongside blue potato, pita chips or crudités.