Isolation between the ports of a two-port terahertz (THz) multi-input, multi-output (MIMO) dielectric resonator (DR) antenna (DRA) is enhanced using a newly implemented technique which has been numerically analysed. Frustum geometry of DRs can provide the high isolation without requiring the separation distance between the radiators. The minimum isolation between the ports is enhanced to 21 dB in the case of frustum geometry of the DRs which remains around 12 dB in the case of conventional cylindrical DRs over a wide impedance bandwidth of THz. The orthogonal feeding arrangement is utilized to find the polarization diversity in antenna. The operation of antenna with multiple modes equivalent to the vertical electric dipoles of fundamental and higher order offers the radiation patterns with peaks off to the boresight axis which are resultantly organized to find the pattern diversity in antenna. The circuit analysis validates the antenna operation. The radiating surface of the DRs is coated with graphene that can provide the electrically tunable response over a wide frequency range. Setting the adequate surface conductivity of graphene can provide the dual mode operation of antenna with the capability of MIMO and self-diplexing with high gain around 6 dBi. The MIMO parameters like envelope correlation coefficient and diversity gain are found <0.1 and >9.98, respectively.