This paper presents a modeling method for extracavity-pumped terahertz parametric oscillators (TPO) based on stimulated polariton scattering, in which the pumping beam is from a different laser, and the Stokes beam oscillates in its cavity. After suitable approximations and assumptions, the average THz wave amplitude in the nonlinear crystal is expressed as a function of the fundamental and Stokes wave amplitudes. Then the rate equation for the Stokes wave is obtained based on the Stokes wave increment within a cavity roundtrip timescale. After solving the Stokes wave rate equation, the Stokes wave temporal evolution is considered as a known parameter, and the properties of the residual fundamental and terahertz waves are obtained by numerically solving the coupled wave equations. This modeling method is applied to an extracavity-pumped TPO based on MgO:LiNbO3 crystal. The simulation results are basically consistent with the experimental results. The main reasons causing the deviations of the simulation results from the experimental results are analyzed. To the best of our knowledge, this is the first time to perform the modeling for extracavity-pumped Q-switched TPOs.