Terahertz (THz) waves, occupying the frequency range of 0.1 to 10.0 THz, hold great potential for sensing and communication, as well as on-chip manipulation. However, the weak response of natural materials to THz waves fundamentally limits the development of high-performance THz devices. Metamaterials and their two-dimensional counterparts, metasurfaces, offer a promising route to enhance and manipulate THz waves. Nevertheless, most existing THz devices support only single functions, such as frequency tuning or amplitude modulation, making them difficult to adapt to diverse application scenarios. In contrast, multifunctional integrated THz devices that address complex real-world needs have attracted growing research interest. Ge₂Sb₂Te₅(GST) is a non-volatile phase-change material that reversibly switches between phases under optical, electrical, or thermal stimulation. SrTiO₃(STO) is a temperature-sensitive dielectric material; its permittivity varies with temperature, allowing modulation of the local electromagnetic environment. To realize a switchable multifunctional THz device, we propose a metasurface integrating GST and STO. The structure consists of a polymer substrate, an STO dielectric layer, and a gold film etched with π-shaped slot structures filled with GST. When GST is in different states, the metasurface achieves tunable slow-light and switchable filtering functions. When GST is in its insulating state, the coupling between bright and dark modes produces an electromagnetically induced reflection (EIR)-like effect. Based on a coupled harmonic oscillator model, the tuning mechanism is elucidated: temperature variation modulates the STO permittivity, thereby altering the effective refractive index of the medium surrounding the dark mode, and thus moves the resonance frequency. As a result, both the EIR reflection window and the slow-light effect are tunable across 1.43-1.79 THz, with a maximum group delay of 5.25 ps. When GST switches to the metallic phase, the system transitions to a dipole resonance mode, and the functionality shifts to an optical switch and stopband filter. The optical switch achieves a modulation depth of 90%, while the stopband filter exhibits a 3 dB bandwidth of 0.22 THz and maintains high thermal stability over the operating temperature range. Furthermore, we explore its refractive-index sensing potential and analyze the impacts of structural parameter variations on the device performance. The proposed design shows strong potential for optical buffering, optical switching,