1. Place beet and onion pieces in medium bowl; toss to combine. Set aside. Working over a bowl, cut away peel, pith, and outer membranes from oranges; cut flesh away from membranes, collecting sections and juice in bowl. Squeeze juice from membranes before discarding them. Set fruit and juice aside.

2. In a small saucepan over medium heat, bring vinegar, sugar, and 1/2 cup water to a boil. Stir until sugar is dissolved, about 2 minutes. Pour liquid over reserved beet-and-onion mixture; let stand until vinegar mixture reaches room temperature, about 30 minutes. Add reserved orange segments, juice, and dried cranberries; toss gently.

3. Place watercress in large serving bowl. With a slotted spoon, spoon beet mixture over watercress. Serve.