As-S sulfide glasses with a high optical quality were prepared via purification of high-purity elemental raw materials and chemical distillation of the glass melt. Based on the glasses, a multimode step-index optical fiber was drawn by a rod-in-tube technique. The transmission loss of the fiber was measured, its performance of transmitting high-power mid-infrared laser was characterized, and the laser damage mechanism was analyzed. The results show that the fabricated fiber with a core diameter of ~200 μm and a numerical aperture of ~0.35 has transmission losses of ~0.25 dB/m and ~0.35 dB/m at 2 μm and 4.6 μm, respectively. Under effective cooling condition, the fiber can withstand ~120 W incident power of 2 μm continuous wave laser, and deliver transmitted power of ~63 W. According to the theoretical analysis, the damage of the fiber at a high laser power is related to the distribution of nano-sized heterophase inclusions (NHPI) in the core glass. The heat accumulation could occur in the region at a high concentration of NHPI, resulting in the thermal damage of the fiber.