Trim all visible fat from the meat and place it in a slow cooker.
In a medium bowl, combine the onion, water, mushrooms, ketchup, wine, mustard, Worcestershire sauce, salt, pepper and garlic. Pour the mixture over the meat. Cover and cook on low about 8 hours.
Remove the meat from the slow cooker, wrap it in foil and keep warm.
Turn slow cooker control to high.
In a small bowl, dissolve the cornstarch in water; stir it into the slow cooker. Cover and cook on high for 15 to 20 minutes or until slightly thickened.
Slice the beef, and serve the sauce with the meat.