Trim visible fat from pork roast; cut in half so it will fit into slow cooker. Place halves side by side in the bottom of a 5 qt or larger slow cooker.
In a 4 cup glass measure, mix together apple juice, mustard, and chicken broth. Pour mixture over roast. Cover and cook on LOW for 8-10 hours or a thermometer inserted into each roast registers at least 160 degrees.
When roast is cooked, remove meat to a platter; using two forks, shred meat.
In small jar with a lid, shake together cornstarch and water. Slowly pour mixtures - a tablespoon at a time - into the sauce remaining in the cooker. Stir until slightly thickened, about one minute.
NOTE: You may not need all the cornstarch mixture.