Trim roots and stems from beets; scrub with a brush. Peel beets. Cut beets in half lengthwise; cut into 1/4-inch-thick slices. Place beets, 3 orange rind strips, orange juice, and vinegar in a 6-quart pressure cooker. Close lid securely; bring to high pressure over high heat (about 4 minutes). Adjust heat to medium or level needed to maintain high pressure; cook 3 minutes. Remove from heat; place pressure cooker under cold running water. Remove lid.
Drain mixture in a colander over a bowl, reserving 1 cup cooking liquid. Discard the 3 orange rind strips. Combine 1 cup reserved cooking liquid, beets, onions, sugar, grated orange rind, and mustard in a bowl; toss gently. Place 1 cup greens on each of 4 plates; top with beet mixture. Garnish with additional orange rind strips, if desired.