Pulse energy transferred from the peak to wings is inevitable in the process of ultrashort optical pulse amplification due to the accumulation of high nonlinearity, which degrades the temporal pulse quality. The energy-related saturable absorbers are applied to remove the wings of high-energy pulses without causing a severe loss of the peak in this research. A cascaded-saturable-absorbers system is proposed, and the effects of the cascaded order, low-intensity loss coefficient, saturable fluence, relaxation time and input fluence distribution on the pulse wings are numerically investigated, respectively. The obtained results can provide a general guidance of design for high-energy ultrashort pulse cleaning.