Whisk grapeseed oil, soy sauce, yuzu juice, and garlic in a medium bowl. Season dressing to taste with salt and pepper.
Heat olive oil in an extra-large heavy skillet over medium-high heat. Add mushrooms, season with salt, and sauté until wilted and just beginning to brown, about 7 minutes. Add sake; stir to coat, then transfer to a large bowl. Add 5 tablespoons dressing; toss to coat. Season with salt.
Divide greens among plates. Divide mushrooms among plates, mounding slightly in center atop greens. Drizzle remaining dressing over greens and mushrooms. Garnish with chives and serve.
