Dynamically switchable half-/quarter-wave plates have recently been the focus in the terahertz regime. Conventional design philosophy leads to multilayer metamaterials or narrowband metasurfaces. Here we propose a novel design philosophy and a VO2-metal hybrid metasurface for achieving broadband dynamically switchable half-/quarter-wave plate (HWP/QWP) based on the transition from the overdamped to the underdamped resonance. Results show that, by varying the VO2 conductivity by three orders of magnitude, the proposed metasurfaces function can be switched between an HWP with polarization conversion ratio larger than 96% and a QWP with ellipticity close to -1 over the broad working band of 0.8-1.2 THz. We expect that the proposed design philosophy will advance the engineering of metasurfaces for dynamically switchable functionalities beyond the terahertz regime.