Stand a gallon-size zip-lock plastic bag in a bowl. Pour in soy sauce, sugar, onion, sake, mirin, garlic, ginger, pepper, and mustard. Hold bag closed and shake until sugar is dissolved. Add beef; seal bag. Chill at least two hours or up to 1 day, turning occasionally.
Lay tri-tip on a lightly oiled barbecue grill over a solid bed of medium coals or medium heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds); close lid on gas grill (discard marinade). Cook, turning every 5 minutes, until rare in center of thickest part (cut to test; 125° to 130° on a thermometer), about 25 minutes, or until as done as you like.
Transfer tri-tip to a cutting board. Let rest about 5 minutes, then cut across the grain into thin, slanting slices.