Remove excess fat from meat. Cut meat into 1-inch pieces.
In a 4 to 5 quart slow cooker combine beef, mushrooms, onion, mustard, garlic, salt and pepper. Stir in beef broth and wine. Cover and cook on low setting for 9 to 10 hours or on high setting for 4 1/2 to 5 hours.
If using low-heat setting, turn to high-heat setting. Combine in a small bowl, sour cream and cornstarch. Stir 1/2 cup of the hot cooking liquid into the sour cream mixture. Return all of the sour cream mixture to the slow cooker and stir well. Cover and cook for 15 minutes more or until thickened. Top each serving with chives.