We investigate the spontaneous emission of a quantum emitter (QE) placed near the twisted hyperbolic metasurfaces (HMTSs) made of graphene strips. We demonstrate that the spontaneous emission can be enhanced distinctly due to the existence of moiré hyperbolic plasmon polaritons (HPPs) supported by the twisted HMTSs. Moreover, the spontaneous emission decay rate can be efficiently modulated by the chemical potential of graphene, the thickness of the dielectric spacer, and the twist angle between two HMTSs. The maximum spontaneous emission is achieved when topological transition occurs. The spontaneous emission will be enhanced as the thickness of the dielectric spacer increases for most cases. In particular, the twisted HMTSs make it possible to flexibly modify the spontaneous emission through the external field. The findings in this work not only extend past studies of twisted photonic structures but also have important applications in optical sensing and integrated photonics.