Understanding the future fate of the Greenland Ice Sheet (GIS) in the context of anthropogenic CO2 emissions is crucial to predict sea level rise. With the fully coupled Earth system model of intermediate complexity CLIMBER‐X, we study the stability of the GIS and its transient response to CO2 emissions over the next 10 Kyr. Bifurcation points exist at global temperature anomalies of 0.6 and 1.6 K relative to pre‐industrial. For system states in the vicinity of the equilibrium ice volumes corresponding to these temperature anomalies, mass loss rate and sensitivity of mass loss to cumulative CO2 emission peak. These critical ice volumes are crossed for cumulative emissions of 1,000 and 2,500 GtC, which would cause long‐term sea level rise by 1.8 and 6.9 m respectively. In summary, we find tipping of the GIS within the range of the temperature limits of the Paris agreement. Plain Language Summary With ongoing carbon dioxide emissions from the burning of fossil fuels, the atmosphere heats up, which has dramatic consequences for the ice sheets on Earth. In this study, we focus on the Greenland ice sheet (GIS), which holds so much ice that a complete melting would cause the global sea level to rise by 7 m. However, future mass loss of the GIS is challenging to predict because it is a non‐linear function of temperature and occurs over long timescales. For this reason, we use CLIMBER‐X, which is a coupled model of the whole Earth system. We find that the GIS features two critical volume thresholds, whose crossing would imply extensive further mass loss so that it would be difficult for the ice to grow back, even in thousands of years. Near these critical ice volumes, the mass loss rates are particularly high, and differences in the total carbon dioxide emission have a large impact. In summary, if cumulative emissions larger than 1,000 Gt carbon are released into the atmosphere, the GIS will shrink below a critical threshold and mass loss will inevitably continue until a substantial part of the ice sheet has melted. Key Points Bifurcation points exist at global mean temperature anomalies of 0.6 and 1.6 K relative to pre‐industrial Mass loss rate and sensitivity to cumulative CO2 emission peak near the equilibrium ice volumes belonging to these temperature anomalies Substantial long‐term mass loss of the Greenland ice sheet for cumulative emissions larger than 1,000 Gt carbon