Using a Cr:ZnS wafer as the saturable absorber, diode-pumped passively Q-switched mode-locking of a Tm:YAP laser at 1976 nm has been realized for the first time, to the best of our knowledge, and nearly 100% modulation depth of Q-switched mode-locking was achieved. The width of the mode-locked pulse was estimated to be about 980 ps with a repetition rate of 350 MHz within a roughly 300-ns-long Q-switched pulse envelope. A maximum output power of 940 mW was obtained, corresponding to the Q-switched pulse energy of 0.55 mJ. The emission wavelength evolution between the continuous-wave and Q-switched mode-locked operations was presented and discussed. The experimental results indicate that the Cr:ZnS absorber is a promising saturable absorber for passively Q-switched mode-locking operation around 2 μm.