Nonlinear optical parametric conversion process based on Stimulated Polariton Scattering (SPS) is an effective way to generate tunable terahertz waves and near-infrared Stokes light with high efficiency. In order to make the SPS process effective, non-collinear phase matching is used to keep the three waves in the crystal at the same phase velocity. Non-collinear phase-matched terahertz wave parametric sources mainly use parametric oscillators and seed-injected parametric generators to achieve frequency limitation and tuning. This paper proposes a new method to achieve non-collinear phase matching of SPS by using two intersecting pump beams to simultaneously excite SPS. The SPS along the transmission direction of the center of the intersection of the pump beams has the same phase matching relationship, and Stokes can obtain the maximum parametric gain and continuous amplification. The SPS in other directions is suppressed by the combined action of a pump beam that satisfies phase matching and a pump beam that does not satisfy phase matching. This method can achieve non-collinear phase matching without relying on a resonant cavity and can be used for short-pulse laser pumping. The basic principle of parametric amplification is studied theoretically, and the gain formula of parametric amplification is derived. Taking cross-pumping based on total reflection of pump light on the side of the crystal as an example, the phase matching relationship of cross-pumping SPS is analyzed, and the phase mismatch of SPS in different transmission directions and the single-pass parametric gain expression of Stokes light are obtained. The gain efficiency curve is obtained through numerical calculation, revealing the physical mechanism of cross-pumping to achieve non-collinear phase matching of SPS. In the experiment, cross-pumping was achieved by grazing incidence of pump light on the side of the crystal at a certain angle to achieve total reflection. By rotating the angle of the crystal, the intersection angle of pump light and phase matching conditions are changed, thereby achieving frequency tuning of Stokes light and obtaining tunable narrow-band Stokes light output. The wavelength tuning range of Stokes light is 1 068~1 076 nm, and the highest output is obtained near 1 071 nm. The measured angle tuning characteristics are consistent with theoretical values, indicating that cross-pumping to achieve SPS phase matching follows the basic principles of nonlinear optical phase matching. The measured line width of Stokes light is 0.17 nm, the lateral divergence angle is 0.053°, and the longitudinal divergence angle is 0.66°. In the experiment, a cascading phenomenon similar to that in a cross-pumped terahertz parametric oscillator was found. The pulse width of Stokes light is related to the energy of the pump light. Within a certain range, the larger the incident pump light energy, the wider the pulse width of Stokes light and the shorter the establishment time. When the pump light energy increases from 8 mJ to 14 mJ, the pulse width of Stokes light increases from 2 ns to 4 ns. The relationship between the output energy of Stokes light and the incident pump light energy was measured. The threshold pump energy for producing Stokes light is about 7 mJ, corresponding to a pump intensity of 120 MW/cm^-1. The highest Stokes light output energy is 1.07 mJ at a pump energy of 15 mJ, corresponding to an energy conversion efficiency of 6.8%, and there is no energy saturation phenomenon as the pump energy increases. Using a silicon prism array to couple out terahertz waves, the relationship between the output energy of THz waves and the pump light energy was measured and compared with the output THz wave energy of a shallow surface cross-pumped terahertz wave parametric oscillator with an external resonant cavity. It is found that the efficiency of cross-pumping SPS increases with increasing pump intensity. It can be expected that under sub-ns short-pulse pumping, due to the crystal's ability to withstand a pump intensity of 2 GW/cm^-1, the gain coefficient can be increased several times, and the efficiency of cross-pumping SPS can be further greatly improved. This research provides a reference for phase matching methods in nonlinear optical processes, especially suitable for short-pulse situations where the pump light pulse width is less than sub-ns.