In a large glass or ceramic pan, combine the soy sauce, sake, sugar, scallions, garlic, lime zest and juice, and mirin and stir to dissolve the sugar.

Add the tuna to the pan and marinate for 11/2 to 3 hours in the refrigerator, turning once during the marinating.

Heat your grill to medium high. Lightly oil the grill or spray with cooking spray.

Remove the fish from the marinade and season with salt and pepper. Grill the tuna for about 2 minutes per side, keeping it rare to medium rare in the center.