Place slivered onion in a bowl. Add cold water to cover and let stand 10 minutes. Meanwhile, slice radishes. Cut cucumber in half lengthwise, scoop out seeds with a spoon, and thinly slice into crescents. Drain onion.
In a large bowl, mix yogurt, lemon juice, cumin seeds, salt, pepper, and all but 2 tablespoons of the mint. Add onion, radishes, and cucumber and mix gently to coat. Cover and chill at least 1 hour or up to 1 day.
Just before serving, stir salad again to combine. Sprinkle with remaining 2 tablespoons mint.