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Due to the ultralow saturation properties of the topological insulator (TI), stable and high-power TI-based solid state has become an important issue. In this paper, using a folding V-shaped laser cavity to minimize the residual pump to the broadband saturable absorber, passive Q-switched operations with high power not only at 1.06 μm but at 1.34 μm as well were demonstrated. The 1.06-μm laser of 150 mW and the corresponding repetition rate and a pulse duration of 28.57 kHz and 576 ns, respectively, were performed. The pulse energy of 5.24 μJ and the corresponding peak power of over 9 W were also estimated. Additionally, the laser at 1.3-μm exhibited a passive Q-switched operation with an average power of as high as 326 mW and a pulse duration of 673 ns. A tunable repetition rate of 75.5 to 116.6 kHz, a pulse energy of 2.8 μJ, and the corresponding peak power of 4.2 W were obtained. In addition, the stability of Q-switched pulses was analyzed. The results experimentally extend the promising application of the 2-D material, i.e., exfoliated TI Bi₂Te₃, in solid-state lasers.