We theoretically provide a scheme for realizing a photonic negative differential transistor (NDT) by using a two-port asymmetric system with cavity exciton polaritons. In such a hybrid optomechanical system, the transmission of the probe light can be completely regulated by the pump field. Interestingly, the resonance transmission curve of probe light has a negative (positive) slope to the pump intensity, which depends on the coupling among excitons, photons and phonons. Therefore, the probe transmission exhibits the characteristic of negative (positive) differential transistors. The transmission spectrum of probe fields is modified by Stokes and anti-Stokes scattering effects, resulting in the output probe light be either attenuated or amplified. Moreover, we find that the transmission of pump fields has a bistability characteristic with appropriate parameters due to nonlinear effects. Our results open up exciting new possibilities for designing a photonic NDT, which may be applied to implement polariton integrated circuits.