Whisk wine, soy sauce, garlic, and 1 teaspoon dry mustard in large glass baking dish.
Add tri-tip and turn to coat with marinade.
Let stand at room temperature 30 minutes, turning meat occasionally.
Meanwhile, whisk honey, 2 tablespoons water, 1/4 teaspoon salt, and remaining 2 tablespoons dry mustard in small bowl to blend; set sauce aside.
Preheat oven to 450°F.
Remove tri-tip from marinade; pat dry with paper towels.
Place tri-tip on large rimmed baking sheet; sprinkle with salt and pepper. Arrange green onions and mushrooms around meat; drizzle onions and mushrooms with olive oil. Roast 12 minutes. Turn meat, onions, and mushrooms over; roast until vegetables are tender and instant-read thermometer inserted into center of meat registers 125°F for medium-rare, about 12 minutes longer.
Place mushrooms and green onions on platter.
Cut meat into 1/4-inch-thick slices; arrange atop green onions and mushrooms.