In this paper, a dual-mode multifunctional switching terahertz metasurface polarization converter based on vanadium dioxide (VO2), photosensitive semiconductor silicon (Si) and graphene is designed. The converter can switch between transmission and reflection modes by adjusting the state of VO2. In the insulating state of VO2, the converter operates in transmission mode and performs linear-to-linear polarization conversion (LTL-PC) with a relative bandwidth of 166.0 %. Conversely, when VO2 is in the metallic state, the converter works in reflection mode. By adjusting the pump light intensity to modulate the state of Si, linear-to-circular polarization conversion (LTC-PC) and LTL-PC function can be achieved. Moreover, the Fermi level of graphene can be adjusted via electrostatic gate to further enhance the working bandwidth of the converter. In reflection mode, the relative bandwidths for LTL-PC, linear to left-circularly and right-circularly polarization conversion are 98.1 %, 87.0 % and 4.0 %, respectively. The metasurface polarization converter proposed in this paper has a variety of functions and a variety of control modes, and has the advantages of high polarization conversion rate and wide operating band, showing great potential in switching and tunable wideband terahertz converters and related applications.