We demonstrate a high peak power, all-fiber passively Q-switched Tm-doped laser operating at 1940 nm for applications in soft tissue ablation. High peak power and passive Q-switching were achieved via a clad pumped gain fiber and a smaller core Tm-doped fiber saturable absorber respectively. Clad pumping was achieved via two 30 W diodes operating at 793 nm. At 50.7 W of pump power, laser pulses with 140 ns FWHM duration and average power of 14.5 W were obtained at a repetition rate of 328 kHz which corresponded to a pulse energy of ~44 µJ and a peak power of ~316 W. The laser had a narrow 0.14 nm linewidth at the maximum output power. The laser was used to cut chicken breast as well as ovine cortical and subcortical brain tissues and average ablation efficiencies of 29, 40 and 42% were obtained, respectively. Cutting speeds of 10 mm/s for ovine brain tissue and 5 mm/s for chicken breast were achieved. Further resection experiments were performed with the target tissue placed under a thin layer of water. A resected volume with length, width and depth of 5 mm, 2.5 mm, and 2.8 mm were obtained, corresponding to a resection rate of ~0.58 mm/s. To our best knowledge, this is the first report of an all-fiber clad-pumped passively Q-switched Tm-doped fiber laser with a core mismatched saturable absorber being used for tissue ablation experiments.