We present the discovery of two distinct classes in the Swift short duration gamma-ray bursts (S-GRBs) from the X-Ray Telescope (XRT) X-ray afterglow light curve. We find that about 40% of the Swift S-GRBs have an X-ray afterglow light curves which only lasts less than 10(4) seconds after the burst trigger (hereafter short-lived S-GRBs). On the other hand, another 60% of S-GRBs have a long lasting X-ray afterglow light curve which resembles the long duration gamma-ray bursts. We also find that none of the short-lived S-GRBs shows the extended emission in the Burst Alert Telescope (BAT) energy range. We compare the burst properties for both the prompt emission and the afterglow, and discuss the possibility of different progenitors for the Swift short GRBs.