This Nd:BG1-xSxO (Nd:BGSO) crystal was grown using the micro-pulling-down method, and the continuous-wave laser operation of this crystal was demonstrated for the first time, to the best of our knowledge. The maximum output power of 1.038 W was obtained under the absorbed pump power of 3.01 W, which corresponds to a slope efficiency of 31.3%. Bismuth nanosheets were first employed as saturable absorbers to generate a passively Q-switched Nd:BGSO laser. Stable Q-switched pulses with the shortest pulse width of 376.5 ns and the maximum repetition rate of 136.6 kHz were achieved at the absorbed pump power of 3.01 W. The largest pulse energy and highest peak power achieved were 0.94 μJ and 2.48 W, respectively.