Passive Q switching of a Tm:YAP solid-state laser at 1935 nm with Cr:ZnSe and Cr:ZnS polycrystalline saturable absorbers is demonstrated for the first time, to the best of our knowledge. With Cr:ZnS, a maximum pulse energy of 1.85 mJ is obtained for a pulse duration of 35.8 ns, resulting in a peak power of 51.7 kW. With Cr:ZnSe, the achieved pulse energy of 1.55 mJ with a pulse duration of 42.2 ns leads to 36.7-kW peak power. These high pulse energies, together with the unique lasing wavelength at 1935 nm, make this laser a promising tool for biomedical and microsurgery applications.