A tunable terahertz four-port multiple-input-multiple-output (MIMO) graphene microstrip patch antenna with self-multiplexing ability is designed and numerically studied. The top layer of the four-port patch antenna, which is a symmetric cross-shaped graphene patch, is patterned using a cross-slot. Insertion of this cross-slot improved the level of isolation to the order of 50-70 dB in the MIMO mode of operation. The frequency of impedance matching at each port of the designed antenna could be tuned independently by applying an electrostatic potential on the corresponding graphene patch enabling its usage as a MIMO self-diplexing and quadruplexing antenna. The MIMO performance parameters like envelope correlation coefficient, diversity gain, mean effective gain, etc. are found within the acceptable limits. An equivalent circuit model is presented to provide insight into the radiation mechanism and validate the results.