For vinaigrette: In a bowl, combine lime juice, soy sauce, garlic, vinegar, lemon juice, oil and black pepper. Whisk until blended.
For slaw: Toss radish, carrot, unripe papaya, basil and mint with vinaigrette.
Slice chilled tuna into 1/4 in.- (0.5 cm)-thick slices. Place slaw on a plate. Garnish with orange, avocado, ripe papaya and pine nuts. Fan tuna over slaw and drizzle with remaining vinaigrette. Garnish with cilantro.