We present a theoretical study of terahertz (THz) radiation induced by surface plasmon polaritons (SPPs) on a graphene layer under modulation by a surface acoustic wave (SAW). In our gedanken experiment, SPPs are excited by an electron beam moving on a graphene layer situated on a piezoelectric MoS2 flake. Under modulation by the SAW field, charge carriers are periodically distributed over the MoS2 flake, and this causes periodically distributed permittivity. The periodic permittivity structure of the MoS2 flake folds the SPP dispersion curve back into the center of the first Brillouin zone, in a manner analogous to a crystal, leading to THz radiation emission with conservation of the wavevectors between the SPPs and the electromagnetic waves. Both the frequency and the intensity of the THz radiation are tuned by adjusting the chemical potential of the graphene layer, the MoS2 flake doping density, and the wavelength and period of the external SAW field. A maximum energy conversion efficiency as high as ninety percent was obtained from our model calculations. These results indicate an opportunity to develop highly tunable and integratable THz sources based on graphene devices.