Combine first 5 ingredients in a small bowl; stir with a wire whisk until well-blended. Set aside.
Heat oil in a wok or large nonstick skillet over high heat. Add carrot, celery, and onion; stir-fry 2 minutes. Add snow peas, corn, and mushrooms; stir-fry 2 minutes. Add broth mixture; stir-fry 1 minute or until thick and bubbly.