Trim fat from meat. Cut meat into 3/4-inch pieces. Lightly coat large skillet with cooking spray; heat over medium-high heat. Add meat, half at a time; cook and stir until meat is brown. Drain off fat. Set meat aside.
In 3 1/2- or 4-quart slow cooker, combine mushrooms, onion, garlic, salt, and pepper. Sprinkle with tapioca. Add meat. Pour broth and, if desired, wine over all.
Cover and cook on low-heat setting for 8 to 10 hours or on high-heat setting for 4 to 5 hours.
If using low-heat setting, turn to high-heat setting. Stir in sugar snap peas. Cover and cook about 5 minutes more or until snap peas are tender. Stir in cherry tomatoes. If desired, serve meat mixture over hot cooked noodles.