I think he's referring to his "uppers" his upper dentures. He'll take out his dentures and throw it through Mayer's window.

Although Gable strove to be "just a regular guy," few people at first took him seriously; either they thought he "was involved as an actor only," or made him the object of fun. Gable countered the jibes with gags of his own. One morning, shaving with fifty other men, he waved around his dentures, joking, "Look at the King, the King of Hollywood. Sure looks like the Jack now, doesn't he?" He genuinely wanted to relate to his peers, and soon most men regarded him as a "regular fellow." A friend said, "I think those of us who knew Clark Gable as a soldier saw the real man more than anyone else perhaps in his whole lifetime. He was not a movie star to us." The fans disagreed.
http://www.geocities.com/cactus_st/article/article143a.html