The recent development of the terahertz waveguide makes it an excellent platform for integrating many intriguing functionalities, which offers tremendous potential to build compact and robust terahertz systems. In the context of next-generation high-speed communication links at the terahertz band, engineering the dispersion and birefringence of terahertz waves is essential. Here, we experimentally demonstrate subwavelength birefringent waveguide gratings based on the low-loss cyclic olefin copolymer exploiting micro-machining fabrication techniques. Asymmetric cross-section and periodic-structural modulation along propagation direction are introduced to achieve birefringent THz grating for filtering and dispersion compensation. Because of strong index modulation in the subwavelength fiber, a high negative group velocity dispersion of -188 (-88) ps/mm/THz is achieved at 0.15 THz for x-polarization (y-polarization), i.e., 7.5 times increase compared to the state-of-the-art reported to date. Such high negative dispersion is realized in a 43 mm grating length, which is less than half of the length reported until now (e.g., 100 mm). Further, the subwavelength fiber grating filters two orthogonal polarization states and exhibits transmission dips with 8.5-dB and 7.5-dB extinction ratios for x and y polarization, respectively. Our experiment demonstrates the feasibility of using polymer-based terahertz gratings as a dispersion compensator in terahertz communications and steering polarized terahertz radiations for polarization-sensitive THz systems.