The International Ocean Discovery Programme (IODP) and its predecessors generated a treasure trove of Cenozoic climate and carbon cycle dynamics. Yet, it remains unclear how climate and carbon cycle interacted under changing geologic boundary conditions. Here, we present the carbon isotope (δ13C) megasplice, documenting deep-ocean δ13C evolution since 35 million years ago (Ma). We juxtapose the δ13C megasplice with its δ18O counterpart and determine their phase-difference on ~100-kyr eccentricity timescales. This analysis reveals that 2.4-Myr eccentricity cycles modulate the δ13C-δ18O phase relationship throughout the Oligo-Miocene (34-6 Ma), potentially through changes in continental weathering. At 6 Ma, a striking switch from in-phase to anti-phase behaviour occurs, signalling a reorganization of the climate-carbon cycle system. We hypothesize that this transition is consistent with Arctic cooling: Prior to 6 Ma, low-latitude continental carbon reservoirs expanded during astronomically-forced cool spells. After 6 Ma, however, continental carbon reservoirs contract rather than expand during cold periods due to competing effects between Arctic biomes (ice, tundra, taiga). We conclude that, on geologic timescales, System Earth experienced state-dependent modes of climate-carbon cycle interaction.