Abstract Metasurface, spatiotemporal metasurface and tunable metasurface have attracted more and more attention in the fields of communication, polarization image and terahertz detection. Numerous tunable metasurfaces have been proposed recently for generating a diverse array of applications. However, many proposed tunable metasurfaces have been limited to a single state switching function, which has severely hampered their development. In this paper, eight meta-atoms were designed by employing the InSb, that dielectric constant could be modulated by temperature. Consequently, the phase delay of the meta-atoms is various under different temperature. Thus, two thermally tunable metasurfaces were proposed. At 260 K, the InSb-based dynamic vortex beam generator can generate a vortex beam with topological charge of l = 1 at 2.25 THz. Correspondingly, at 180 K, the metasurface exhibits a phase coverage of 4π and the topological charge of generated beam is converted from l = 1 to l = 2. With decreasing of the temperature, the phase gradient between the proposed meta-atom increases. Therefore, a phase gradient metasurface was proposed to generate light beam with adjustable direction. This proposed metasurface could provide a valuable scheme for developing tunable devices and terahertz metasurfaces.