The passively Q-switched mode-locked (QML) operation of a Tm:CaGdAlO4 (Tm:CALGO) bulk laser pumped by a wavelength-tunable Ti:sapphire oscillator using molybdenum disulfide (MoS2) as a saturable absorber was demonstrated. By using an output coupler with 3% transmittance, Q-switched mode-locked operation can be achieved with 3.56 W absorbed pump power. At a pump power of 6.77 W, laser pulses with the maximum average power of 1.44 W were obtained, corresponding to a slope efficiency of 21.3%. The laser delivered pulses centered at 1927 nm with a repetition frequency of 131.6 MHz. The experimental results confirm the promising application of the MoS2 in high-power Q-switched mode-locked solid-state lasers at 2 µm.