Magnesium 2,5-dihydroxyterephthalate (Mg-MOF-74) nanosheets were prepared by liquid-phase exfoliation method. The surface morphology and nonlinear absorption properties of the nanosheets were investigated. Employing the Mg-MOF-74 nanosheets as a saturable absorber, a stable passively Q-switched Tm:YAP laser was successfully realized. Under an incident pump power of 7 W, the average output power of the Q-switched pulses was 1150 mW with a T = 5% output coupler, corresponding to a single-pulse energy of 11.3 μJ and peak power of 25.6 W. Meanwhile, the obtained minimum pulse duration was 313 ns at a repetition rate of 117 kHz with a T = 1% output coupler.