In this paper, magnetoplasmonic manipulation of near-field radiative heat transfer (NFRHT) is realized using two twisted graphene gratings. As a result of the quantum Hall regime of magneto-optical graphene and the grating effect, three types of graphene surface plasmon polaritons (SPPs) modes are observed in the system: near-zero modes, high-frequency hyperbolic modes, and elliptic modes. The elliptic SPPs modes, which are caused by the combined effect of magnetic field and grating, are observed in the graphene grating system for the first time. In addition, the near-zero modes can be greatly enhanced by the combined effect grating and magnetic field, rendering graphene devices promising for thermal communication at ultra-low frequency. In particular, the near-zero modes result in a unique enhancement region of heat transfer, no matter for any twisted angle between gratings. The combined effect of grating and magnetic field is investigated simultaneously. By changing the strength of magnetic field, the positions and intensities of the modes can be modulated, and hence the NFRHT can be tuned accordingly, no matter for parallel or twisted graphene gratings. The magnetic field endows the grating action (graphene filling factors and twisted angles) with a higher modulation ability to modulate the NFRHT compared with zero-field. Moreover, the modulation ability of twist can be tuned by the magnetic field at different twisted angles. In sum, the combined effect of magnetic field and grating provides a tunable way to realize the energy modulation or multi-frequency thermal communications related to graphene devices.