We have analyzed the effect of bias-voltage polarities on the shuttle instability in an asymmetrically nanoelectromechanical single-electron transistor (NEM-SET) using the Wigner phase space approach. The electric-field-induced shift in oscillation equilibrium position together with the asymmetrical tunneling rate leads to the symmetry breaking of electron occupations in the quantum dot for positively and negatively biased directions. The symmetry-broken occupations make the works done by the electric field in different biased directions unequal. As a consequence, the threshold voltage for the onset of shuttle instability is lower for a positive bias voltage than for a negative one. Between two thresholds, the NEM-SET device exhibits a pronounced rectification effect.