Nobody can kick countries off the council, though apparently the General Assembly could decide at one point that it was Mainland China and not Taiwan that represented "China" and so the UNSC seat changed hands (and Taiwan lost its UN membership)

From the 1960s onwards, nations friendly to the PRC, led by Albania, moved an annual resolution in the General Assembly to transfer China's seat at the UN from the ROC to the PRC. Every year the United States was able to assemble a majority of votes to block this resolution. But the admission of newly independent developing nations in the 1960s gradually turned the General Assembly from being Western-dominated to being dominated by countries sympathetic to Beijing. In addition, the desire of the Nixon administration to improve relations with China to counterbalance the Soviet Union reduced American willingness to support the ROC.

As a result of these trends, on October 25, 1971, Resolution 2758 was passed by the General Assembly, withdrawing recognition of the ROC as the legitimate government of China, and recognising the PRC as the sole legitimate government of China. China received support from two-thirds of all United Nations' members and the complete unanimous approval by the Security Council excluding the ROC.

The Resolution declared "that the representatives of the Government of the People's Republic of China are the only lawful representatives of China to the United Nations." Because this resolution was on an issue of credentials rather than one of membership, it was possible to bypass the Security Council where the United States and the ROC could have used their vetoes.

Thus, ROC was expelled from UN.

Bush is a symptom, not the disease.