We investigated the dependence of optical damage to an organic nonlinear optical crystal of 4-dimethylamino-N′-methyl-4′-stilbazolium tosylate (DAST) on the repetition frequency and pulse width of the pump beam used to cause the thermal damage. For a pump beam with a pulse width of 15 ns at a wavelength of 1064 nm, the highest damage threshold of 8.0 J/cm2 was measured for repetition frequencies in the range from 10 to 40 Hz. On the other hand, DAST crystals were easily damaged under the repetition rates from 50 to 100 Hz. For 600-ps pulses, a higher damage threshold that was a factor of 11 to 28 times higher in terms of peak intensity was obtained compared with that of 15-ns pulses. In both the cases of 15-ns pulse duration and 600-ps duration, we demonstrated that the thermal effects in DAST crystals dominated the optical damage, which depended on thermal accumulation and dissipation.