The exposure of high-nonlinearity chalcogenide glass fibers to ultrashort pulses is an important approach for achieving broadband mid-infrared supercontinuum (SC). The average output power of a generated SC is mainly limited by the laser damage threshold (LDT) of the material. In this work, the laser damage characteristics of the germanium-antimony-sulfur (Ge-Sb-S) chalcogenide glass are studied using a laser with a pulse width of 216 fs, a central wavelength of 1030 nm, and a repetition rate of 1-1000 kHz to elucidate the composition dependence of the LDT of the chalcogenide glass as well as the mechanisms of damage to the material exposed to irradiation pulses with different repetition rates. Results show that the LDT of the Ge-Sb-S glass decreases with increasing repetition rate of the irradiation pulse. The glass with high average bond energy is found to have a high LDT, and its stoichiometric composition exhibits optimal resistance to optical damage. When the repetition rate of laser irradiation pulse is less than 10 kHz, the glass is observed to be mainly damaged by avalanche ionization. In contrast, thermal accumulation is the dominant factor promoting damage when the repetition rate of the irradiation pulse exceeds 10 kHz.