Heat grill. In food processor bowl with metal blade, combine all mayonnaise ingredients. Cover; blend until smooth. Place mixture in small bowl. Refrigerate while preparing tuna.
When ready to grill, brush both sides of tuna steaks with olive oil; sprinkle with peppered seasoned salt and cumin. Place on gas grill over medium-high heat or on charcoal grill 4 to 6 inches from medium-high coals. Cook 8 to 12 minutes or until fish flakes easily with fork, turning once. Serve tuna steaks with avocado mayonnaise.