Cylindrical vector-polarized vortex pulses from a passively Q-switched laser are demonstrated. Pump radiation reshaped into a size-controlled annular profile via circular Dammann grating produces an efficient excitation of the LG01 mode. The YAG  /  Nd  :  YAG  /  Cr^4  +  :  YAG composite crystal structure is found to reduce the Q-switching threshold and significantly suppress thermal damage, thus allowing ability to obtain a passively Q-switched pulse. The threshold pumping power is found to be 4.35 W, with a slope efficiency of 23.1%. A maximum peak power of 3.24 kW, maximum pulse energy of 53.46  μJ, pulse width of 17.5 ns, and repetition rate of 2.695 kHz are obtained. Furthermore, a radially polarized output with a polarization degree of 88.9% is confirmed. Finally, mode and polarization tuning are also discussed.