In a food processor, combine the parsley, oregano, mint, 2 tablespoons of the olive oil, the red wine vinegar, garlic, red pepper flakes, and the lemon zest and juice. Process until well chopped, scraping down the bowl as needed. Add the mango and pulse once or twice to combine and lightly chop. Season with salt and pepper, then set aside.
Rub the tuna steaks on all sides with the remaining 1 tablespoon olive oil, then season them with salt and pepper. Grill the steaks for 2 to 3 minutes per side for medium-rare. Serve topped with the salsa.