In bowl, combine juice, oil, sugar, salt, and cayenne pepper.
In medium bowl, combine jicama, radishes, cucumber, and 2 Tbsp. juice mix. Cut 1 avocado into 1/2" pieces. Stir into jicama mix. Top with orange segments. Let stand 10 minutes. Thinly slice remaining avocado.
In large serving bowl, toss greens with remaining juice mix. Top with jicama mix. Garnish with avocado slices.