Using a mandoline or sharp knife, thinly slice the white part of the fennel, the radishes, and cucumber. Add the vegetables to a large bowl and make the vinaigrette.
In a small bowl, combine mandarin juice, red wine vinegar, garlic, salt, and pepper. Slowly stream in olive oil while whisking. Whisk vinaigrette until thoroughly combined. Drizzle the desired amount of dressing over the veggies. Chop the fronds of the fennel and use it to garnish your salad.
Serve immediately or let it chill for a while to let the flavors meld.