In a large saucepan, simmer beets in 3 in. (8 cm) water and half of the vinegar, covered. Cook until beets are tender and can be pierced with a paring knife, about 40 min. Uncover and cool beets in the cooking liquid, about 20 min. Peel and cut beets into 1/2-in. (1 cm) pieces.
In a bowl, mix the remaining ingredients and toss with the beets. Set aside for 30 min. to marinate before serving.