In this paper, we propose a graphene-based metasurface that exhibits multifunctions including tunable filter and slow-light which result from surface plasmon polaritons (SPPs) of graphene and plasmon induced transparency (PIT), respectively. The proposed metasurface is composed by two pairs of graphene nano-rings and a graphene nanoribbon. Each group of graphene rings is separately placed on both sides of the graphene nanoribbon. Adjusting the working state of the nanoribbon can realize the functional conversion of the proposed multifunctional metasurface. After that, in the state of two narrow filters, we put forward the application concept of dual-channel optical switch. Using phase modulation of PIT and flexible Fermi level of graphene, we can achieve tunable slow light. In addition, the result shows that the graphene-based metasurface as a refractive index sensor can achieve a sensitivity of 13670 nm/RIU in terahertz range. These results enable the proposed device to be widely applied in tunable optical switches, slow light, and sensors.