RESUMEN
We propose a scheme for generating nonreciprocal strong mechanical squeezing by using two-tone lasers to drive a spinning optomechanical system. For given driving frequencies, strong mechanical squeezing of the breathing mode in the spinning resonator can be achieved in a chosen driving direction but not in the other. The nonreciprocity originates from the Sagnac effect caused by the resonator's spinning. We also find the classical nonreciprocity and the quantum nonreciprocity can be switched by simply changing the angular velocity of the spinning resonator. We show that the scheme is robust to the system's dissipations and the mechanical thermal noise. This work may be meaningful for the study of nonreciprocal device and quantum precision measurement.