In various practical applications, the demand for switchable metasurfaces with versatile functionalities has grown significantly. This paper proposes a graphene-based metasurface that offers independent control over all three electromagnetic (EM) wave modes (i.e., reflection, transmission, and absorption) as well as the polarization state for both reflection and transmission modes, all achieved in real-time at terahertz frequency. The metasurface is designed with a multilayer structure, comprising quartz, gold, and graphene. Two graphene sheets are placed at the beginning and end of the structure to control specific functionalities. By dynamically adjusting the chemical potential of each graphene sheet, the proposed metasurface can manipulate all three EM wave modes and convert linear to circular polarization independently for both reflection and transmission modes. Additionally, the metasurface can switch from polarization conversion to without polarization conversion of the reflected wave by adjusting the chemical potential of graphene. Due to its numerous switchable functions and a high degree of freedom, the presented metasurface has the potential to be used in wireless communication, biomedicine, and optoelectronic devices.