A dual-wavelength continuous-wave (CW) and passively Q-switched alexandrite laser based on a MoS2 saturable absorber (SA) operating at 736.7 nm and 752.8 nm with a simple and compact 18 mm plano–plano resonator is reported. In the CW mode, the output power is 1014 mW at the linear-polarized pump power of 5.44 W, with a slope efficiency of 28.7%. In the pulsed operation, the narrowest pulse width and the maximal peak power are 154 ns and 10.6 W, respectively. This laser can be used to generate 8.71 THz-wave light based on a suitable nonlinear optical crystal.