Energetic, statistical, and temporal characteristics of a picosecond KGW:Nd laser based on the Sagnac interferometer are studied. All experiments are provided in comparison with the traditional linear cavity. The effect of stimulated Raman scattering suppression in such a specific cavity was found. Stimulated Raman scattering in KGW dumped all output parameters in the laser with a linear cavity. A new cavity scheme can solve such problems and provide for good output handling. It is shown that output pulse duration is larger in the proposed scheme compared with a linear cavity but other characteristics are much better.