Arbitrary control and dynamic tuning of circularly polarized (CP) wave are of great significance to photonic research and application. Here, a terahertz switchable metasurface is designed with bifunctional properties based on a mixed structure of graphene and vanadium dioxide (VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). The design consists of VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> strips, topas spacer, VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> film, graphene patch, topas spacer, and metallic film. When VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is metal, this metasurface realizes photonic spin Hall effect (PSHE) for CP wave in a wide frequency band of 0.7-1.5 THz. When VO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is insulator, the design behaves as an absorber. It has a broadband absorption with more than 90% absorptance in the range of 0.48-1.88 THz, and there are two resonant peaks with ~100% absorptance at 0.92 THz and 1.74 THz. Meanwhile, absorption bandwidth and intensity can be dynamically tuned by changing Fermi energy level of graphene. Besides, broadband absorption is robust against incident angle. Our design may promote the realization of terahertz switchable and multifunctional metasurfaces.