We have experimentally demonstrated passively Q-switched (PQS) stimulated Raman scatting (SRS) emissions in an a-cut YVO4 Raman crystal in a coupled cavity, using a Yb:YAG/YAG/Cr4+:YAG/YAG composite crystal to generate the PQS fundamental laser, for the first time, to our best knowledge. At the incident pump power of 6.30 W, the Stokes average output power of 0.42 W was achieved. Due to the cascaded Raman effect, four first-Stokes lines operating at 1092.6 nm, 1125.4 nm, 1135.1 nm and 1157.0 nm and three second-Stokes lines operating at 1210.6 nm, 1263.2 nm and 1290.1 nm were generated simultaneously. It is noted that the spectral broadening of the fundamental field was observed. With the inclusion of an etalon in the fundamental cavity to suppress the spectral broadening, the average output power of the Stokes lines increased to 0.49 W and the maximum pulse energy was enhanced up to 84.30 μJ, corresponding to the diode-to-Stokes conversion efficiency of 7.78%.