Toast the cumin seeds in a small dry skillet over medium heat, stirring, until fragrant and a shade darker, 1–2 minutes; cool, then grind to a fine powder in a spice grinder or mortar.
Grate the cucumber on the large holes of a box grater. Squeeze firmly by the handful or in a clean towel to remove excess liquid until no drips remain.
In a medium bowl, whisk the yogurt with the water until smooth and creamy, thinning to a pourable but not runny consistency.
Stir in the grated cucumber, ground cumin, salt, black pepper, cilantro, and mint until evenly combined.
Taste and adjust salt. Cover and chill 15–30 minutes for flavors to meld, stirring before serving. Serve cold alongside spicy mains or rice dishes.