In this Letter, the fabrication of large-scale (50.8 mm in diameter) few-layered MoS2 with physical vapor deposition on sapphire is described. Open-aperture Z-scan technology with a home-made excitation source at 2275 nm was applied to explore its nonlinear saturable absorption properties. The as-grown few-layered MoS2 membrane possessed a modulation depth of 17% and a saturable intensity of 1.185 MW cm-2. As a consequence, the deposited MoS2 membrane was exploited as a saturable absorber to realize a passively Q-switched Tm:YAP laser for the first time, to the best of our knowledge. Pulses as short as 316 ns were generated with a repetition rate of 228 kHz, corresponding to a peak power of 5.53 W. Results confirmed that the two-dimensional layered MoS2 could be beneficial for mid-infrared photonic applications.