We propose a theoretical scheme to achieve a nonreciprocal polaritonic photonic transistor by using a spinning microresonator coupled to a tapered fiber. In such a nonreciprocal device, owing to the combination of Sagnac effects and Stokes or anti-Stokes scattering, the transmission of probe light in clockwise and counterclockwise directions exhibits clockwise (counterclockwise) unidirectional amplification, bidirectional amplification, and bidirectional attenuation, simultaneously accompanied by unidirectional slow-fast light, bidirectional fast light, and bidirectional slow light, which can be effectively modulated by pump fields and couplings among excitons, photons, and phonons. In particular, we also discover perfect unidirectional transmission, i.e., the transmission in the opposite direction is completely blocked, and fast-slow light switching by appropriately regulating pump fields, which is optimal for signal isolation and controllable group advance-delay switching. Therefore, our proposed nonreciprocal photonic transistor is an excellent multifunctional device with various amplification-attenuation transmission and fast-slow light nonreciprocities. Our results provide an opportunity to engineer multifunctional nonreciprocal photonic devices, which may be useful for building integrated photonic circuits, chiral quantum technologies, and quantum communication networks. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Integrated opticsLight propagation, transmission & absorptionNon-reciprocal transmissionNonlinear opticsOptomechanicsOptical microcavities