Heat oil in a large nonstick skillet over medium-high heat. Add ginger and garlic; stir-fry 30 seconds. Add turnip and rutabaga; stir-fry 1 minute or until crisp-tender. Add sugar snap peas; stir-fry 30 seconds.
Combine broth, soy sauce, cornstarch, and mirin in a small bowl; add to pan. Bring to a boil; cook 1 minute, stirring constantly.