Integrating multiple functionalities into a single device is a striking field in metasurfaces. One promising aspect is polarization-dependent meta-devices enabled by simultaneous phase control over orthogonally polarized waves. Among these, Pancharatnam-Berry (PB) metasurfaces have drawn enormous interest owing to their natural and robust phase control ability over different circularly polarized waves. However, the phase responses are locked to be opposite with each other, resulting in interrelated functionalities under the circularly polarized incidence. Here, a generic designing method based on transmission-type dielectric metasurfaces is proposed in the terahertz regime, which breaks this relation by further incorporating dynamic phase with geometric phase, namely, spin-decoupled phase control method. We demonstrate this method by designing and characterizing an efficient multifunctional meta-grating, which splits different circularly polarized waves to asymmetric angles under normal incidences. More importantly, we promote this method by designing several multiplexed meta-gratings for applications of asymmetric polarization generation, which can convert arbitrary linearly polarized wave to two different linearly polarized waves with nearly equal strength and split them to asymmetric angles with a polarization-insensitive efficiency. The designing strategy proposed here shows an impressive robustness and a great flexibility for designing multifunctional metasurface-based devices and opens new avenues toward modulation of polarization states and the application of metasurfaces in beam steering and polarization multiplexing systems.