A diode-pumped Tm,Ho:KLu(WO4)2 microchip laser passively Q-switched with a Cr:ZnS saturable absorber generated an average output power of 131 mW at 2063.6 nm with a slope efficiency of 11% and a Q-switching conversion efficiency of 58%. The pulse characteristics were 14 ns/9 μJ at a pulse repetition frequency of 14.5 kHz. With higher modulation depth of the saturable absorber, 9 ns/10.4 μJ/8.2 kHz pulses were generated at 2061.1 nm, corresponding to a record peak power extracted from a passively Q-switched Tm,Ho laser of 1.15 kW. A theoretical model is presented, predicting the pulse energy and duration. The simulations are in good agreement with the experimental results.