Set diced cucumbers in colander lined with a tea towel to drain surplus liquid.
In a small bowl, combine garlic and mint. In a large bowl, beat yogurt and milk together until smooth with a whisk or a hand blender on medium speed. Fold in garlic-mint mixture with a spatula. Add cucumbers to bowl and season to taste with salt. Cover and chill overnight or for several hours. Once soup is chilled, check seasoning and add more sault to taste if desired. Serve in chilled bowls, trimmed with extra chopped cucumber and mint.