Ion bombardment of carbon materials is known to cause erosion with energies far below the threshold energy of physical sputtering, as well as at temperatures below the threshold of thermal desorption. Generally regarded as chemical sputtering, this effect, and factors contributing to it, are not well understood. We use classical molecular-dynamics simulations, capable of realistically describing bond formation and breaking, to study amorphous hydrogenated carbon surfaces under low-energy hydrogen bombardment. We present a swift chemical sputtering mechanism which can explain the experimentally observed characteristics of erosion by low-energy ion irradiation. We also show how the difference in the surface hydrogen concentration and carbon coordination fractions at various temperatures affect the carbon sputtering yield.