Cascaded stimulated polariton scattering (SPS) under powerful picosecond pumping of 532 nm wavelength was investigated in a single pass of a KTP (KTiOPO4) crystal. Under ordinary polarization of the pump wave (relatively XOZ-plane) parametric scattering in the KTP crystal was observed. By rotation of the pump wave polarization (from ordinary to extraordinary), this scattering gradually transforms into polariton scattering. Polariton signal components (spots) with gaps between them were registered at external angles of ~2° between the neighboring spots. Five polariton signal components were detected above the pump beam, with a frequency difference between neighboring cascaded components of ~188 cm−1 (5.64 THz). The wavelength of each next component increased regularly with the angle between this component and the pump wave, so this regular sequence of polariton signal components can be regarded as a cascaded SPS.