For salsa, in a bowl, combine the carrots, mango, lime juice, chives, 1/8 teaspoon salt, 1/8 teaspoon pepper, coriander and cumin; set aside. Sprinkle tuna steaks with remaining salt and pepper.
Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack. Grill tuna, covered, over medium heat or broil 4 in. from the heat for 5-7 minutes on each side or until medium-rare or until slightly pink in the center. Serve with salsa.