Passively Q-switched self-Raman laser oscillations in the $\mathrm{Sr}\mathrm{Mo}{\mathrm{O}}_4:{\mathrm{Nd}}^{3+}$ crystal optically pumped by a laser diode (LD) at $804\mathrm{nm}$ are demonstrated for the first time to our knowledge. Output parameters of LD-pumped $\mathrm{Sr}\mathrm{Mo}{\mathrm{O}}_4:{\mathrm{Nd}}^{3+}$ laser were investigated in free-running, passively Q-switched, and self-Raman regimes of laser operation, over a wide range of pulse repetition rates $(8.5–85\mathrm{kHz})$ . A pulse energy of $21\mu \mathrm{J}$ was measured in the self-Raman regime at $1163\mathrm{nm}$ (first Stokes) wavelength, which is 6 times higher than that for the $\mathrm{Gd}\mathrm{V}{\mathrm{O}}_4:{\mathrm{Nd}}^{3+}$ self-Raman laser of similar design.