The Indonesian Throughflow (ITF) serves as the sole tropical interocean conduit in the global ocean circulation, playing a key role in the Earth's climate system. Climate models suggest that global warming will lead to a slowdown of the ITF, yet historical observations reveal a contrary trend. Based on CMIP6 simulation data, we find that the ITF's response to rising atmospheric CO₂ concentrations is nonlinear, characterized by an abrupt weakening after crossing the first tipping point and reaching a new equilibrium state with low ITF transport after a second tipping point. The weakening of the ITF can be explained by the response of its haline and thermal components to increasing CO₂ concentrations, which is closely linked to the nonlinear response of wind forcing and precipitation to external CO₂ forcing. The changes in the ITF between the two tipping points correspond to an "Exchange state," "Transition state," and "Isolate state" of the ocean system comprising the Indian and Pacific Oceans, which in turn correspond to potentially significant differences in the Indo-Pacific oceanic and climatic patterns. Notably, the current atmospheric CO₂ concentration has already reached the first tipping point, and although uncertainties exist in numerical simulations, this suggests that a rapid decline of the ITF and a state shift in the Indo-Pacific maritime region are likely imminent. These findings hold significant implications for understanding climate tipping elements and global ocean circulation under global warming.