Polarization switching and hysteresis are observed in a semiconductor laser with a two‐armed polarization‐sensitive external cavity. An intracavity polarization‐dependent saturable absorber is placed asymmetrically in one of the two arms of the external cavity so that one polarization mode is saturated more strongly than the other. The observed phenomena can be explained by the complementary processes of competition in the gain region and the polarization‐dependent saturable loss in the external cavity. This mechanism is potentially useful as the basis of a two‐mode switchable and bistable diode laser for applications as high‐speed optical memories and logic gates.