Recent observations of the Small Magellanic Cloud (SMC) have revealed that the HI gas shows a significant amount of rotation (V_c 60 km/s), while no or little rotation is evident for the old stellar populations. We suggest that this unique kinematical difference between these components in the SMC can be caused by a major merger event which occurred in the early stage of the SMC formation. Our simulations show that dissipative dwarf-dwarf merging can transform two gas-rich dwarf irregulars into a new dwarf, which consists of a spheroidal stellar component and a rotating extended HI disk. The remnant of this dwarf-dwarf merging shows significantly different kinematics between stars and gas, in the sense that a gas disk rotates rapidly while a stellar component shows little rotation. We thus suggest that the simulated dwarf having a dynamically hot spheroid and an extended gas disk finally evolves into the present SMC after efficient stripping of the outer gas via tidal fields of the Galaxy and the Large Magellanic Cloud. We also suggest that spatial distributions and kinematics of RGB and AGB stars with different ages in the possible spheroidal component of the SMC can provide valuable information on whether and when a past major merger event really occurred in the SMC. Comment: 13 pages, 4 figures (three color), ApJL in press