All solid-state microchip lasers having the advantage of short cavity lengths give them tremendous potential as pulsed devices for short pulse laser generation. In this work, by constructing a compact microchip-like laser resonator, we have demonstrated continuous-wave (CW) Pr,Mg:SrAl12O19 (SRA) lasers at 622 nm and 643 nm, respectively with maximum output powers of 0.69 W and 1.18 W with excellent beam qualities, which is believed to be the highest powers that have achieved in Pr3+ microchip lasers. Based on this CW opeation, we, by using a Co:LMA saturabel absorber, have further demonstrated passively Q-switched operation of the two lasers. The shortest pulse widths reached about 28.5 ns (for the 622 nm laser) and 31.9 ns (for the 643 nm laser), which are relatively short pulse time durations for passively Q-switched Pr3+ lasers thanks to the compact laser configuration. This work has proposed a simple route for achieving compact high-power CW and short-pulse Q-switched visible lasers.