Remove stems from mushrooms and discard or save for another use. Wipe caps clean with a dry towel.
In a bowl, combine the pork, turnip, soy sauce, water chestnuts, salt, and sugar until thoroughly mixed. Spoon stuffing tightly into mushroom caps. Arrange in a steamer basket, stuffing side up, over boiling water. Cover, and cook for 30 minutes. Serve hot.