When peeling raw beets, use gloves or hold with a paper towel to keep your hands from getting stained.
Preheat oven to 400 degrees. In an 8-inch square baking dish, toss beets with 2 tablespoons each vinegar and water. Drizzle with oil; season with salt and pepper. Cover with foil; roast until tender and caramelized, about 50 minutes.
Meanwhile, mix parsley, mint, capers, 1 1/2 teaspoons vinegar, 1/2 cup oil, and 1/4 teaspoon salt. Place grapefruit slices with beets on a platter; drizzle with salsa verde. Season with salt and pepper; serve room temperature.