We demonstrate a physical mechanism for terahertz (THz) generation from surface plasmon polaritons (SPPs). In a structure with a bulk Dirac semimetals (BDSs) film deposited on a dielectric substrate, the energy of the asymmetric SPP mode can be significantly enhanced to cross the light line of the substrate due to the SPP-coupling between the interfaces of the film. Therefore, the SPPs can be immediately transformed into Cherenkov radiation without removing the wavevector mismatch. Additionally, the symmetric SPP mode can also be dramatically lifted to cross the substrate light line when a buffer layer with low permittivity relative to the substrate is introduced. In this case, dual-frequency THz radiation from the two SPP modes can be generated simultaneously. The radiation intensity is significantly enhanced by over two orders due to the field enhancement of the SPPs. The radiation frequency can be tuned in the THz frequency regime by adjusting the beam energy and the chemical potential of the BDSs. Our results could find potential applications in developing room temperature, tunable, coherent, and intense THz radiation sources to cover the entire THz band.