The successive phase transitions of the pyrochlore oxide Cd2Re2O7 are studied by polarizing microscopy and magnetic susceptibility measurements. The formation of twin domains is visualized in the polarizing images of a pristine (111) crystal surface upon cooling through the cubic-to-tetragonal transition at Ts1 ~ 200 K. Moreover, a dramatic change in the twinning pattern is observed at Ts2 ~120 K, which suggests that the tetragonal c axis flips as the strain changes its direction at the tetragonal-to-tetragonal transition. Magnetic susceptibility measurements reveal significant domain alignment upon cooling across Ts1 and Ts2 in a magnetic field of 7 T, which are due to ~10% anisotropy in the magnetic susceptibility for the low-temperature phases. Interestingly, the anisotropy is reversed at Ts2: c{hi}c < c{hi}a above Ts2 and vice versa below Ts2.