We report a transmission electron microscopy (TEM) study on the damage produced by the focused ion beam (FIB) etching for small Bi2Sr2CaCu2Oy (Bi2212) intrinsic Josephson junctions (IJJs). The selected area diffraction patterns of TEM images demonstrate that the FIB damage causes the formation of an amorphous layer. The thickness of FIB damage is at least 30 nm for the Ga+ ion beam emitted at 50 pA and 30 kV, independent of the incident direction of the Ga+ ion beam. We also confirmed that the damage or the redeposition due to the FIB etching was effectively removed by the additional irradiation of Ar ions after the FIB etching. This suggests the advantage of the combinatorial method of the FIB and Ar-ion etchings in the successful fabrication of small and high-quality IJJs.