Currently, terahertz metamaterials are studied in many fields, but it is a major challenge for a metamaterial structure to perform multiple functions. This paper proposes and studies a switchable multifunctional multilayer terahertz metamaterial. Using the phase-transition properties of vanadium dioxide (VO₂), metamaterials can be controlled to switch transmission and reflection. Transmissive metamaterials can produce an electromagnetically induced transparency-like (EIT-like) effect that can be turned on or off according to different polarization angles. The reflective metamaterial is divided into I-side and II-side by the middle continuous VO₂ layer. The I-side metamaterials can realize linear-to-circular polarization conversion from 0.444 to 0.751 THz when the incident angle of the y-polarized wave is less than 30°. The II-side metamaterials can realize linear-to-linear polarization conversion from 0.668 to 0.942 THz when the incident angle of the y-polarized wave is less than 25°. Various functions can be switched freely by changing the conductivity of VO₂ and the incident surface. This enables metamaterials to be used as highly sensitive sensors, optical switches, and polarization converters, which provides a new strategy for the design of composite functional metamaterials.