Crunchy and colorful, this is an ideal first-course salad. Be sure to grate the peel from the tangerines before cutting the fruit into slices.
Finely grate enough peel from tangerines to measure 1 teaspoon; place in small bowl and reserve for dressing. Using sharp knife, cut off top and bottom of each tangerine, then cut off all peel and white pith, following contour of fruit. Cut tangerines vertically in half, then crosswise into 1/4-inch-thick slices; set aside.
Combine 2 tablespoons finely chopped radishes, 1 tablespoon chopped red onion, lemon juice, and grated tangerine peel in small bowl; let stand 5 minutes. Whisk in extra-virgin olive oil. Season salad dressing to taste with coarse kosher salt and freshly ground black pepper.
Combine tangerine slices, radish slices, onion slices, fennel slices, arugula leaves, and chopped fresh mint in large bowl; sprinkle with coarse kosher salt. Drizzle dressing over salad and toss to coat thoroughly. Transfer salad to large shallow bowl and serve.