Heat a small, heavy skillet over medium heat. Toast cumin seeds in hot skillet until darkened and fragrant, about 5 minutes; pour into a wide bowl to cool.
Grind cumin seeds in a mortar and pestle into a fine powder.
Put yogurt in a bowl and beat lightly with a fork or whisk until smooth and creamy.
Stir toasted cumin seeds, cucumber, mint, salt, and cayenne pepper into the yogurt; season with black pepper.