1Whisk first 3 ingredients in small bowl to blend, adding more wasabi paste if desired. Cover and refrigerate.
2Whisk teriyaki sauce, soy sauce, and rice vinegar in small bowl to blend. Place tuna steaks in resealable plastic bag. Add teriyaki mixture; seal bag. Turn bag to coat. Let stand at room temperature 30 minutes, turning bag occasionally.
3Brush grill with vegetable oil.
4Prepare barbecue (medium-high heat). Drain tuna steaks. Grill tuna to desired doneness, about 4 minutes per side for medium.
5Top each tuna steak with about 2 tablespoons wasabi mayonnaise and serve.