Two Nd∶YAG rods are opposed and offset pumped by two half-cylinder laser diode array for uniform pumping and heat releasing, to improve the laser beam quality and output stability of the passively Q-switched laser side-pumped by laser diode under transfer cooling conditions. The effect of transverse-mode structure on passively Q-switched stability is experimentally studied. An unstable corner-cube prism-Gaussian output mirror cavity is studied. The laser beam quality of the device is improved greatly, as well as the passively Q-switched laser stability, and the mechanical stability of resonator. A practical engineering instrument with high stability and high beam quality is developed, with repetition frequency of 20 Hz, single-pulse energy of 64 mJ, pulse width of 7 ns, stability better than ±4.5%, beam divergence of 0.6 mrad, and optical-optical efficiency of 9.1%.