The long-term evolution of the Greenland Ice Sheet (GrIS) remains a major source of uncertainty in projections of future sea-level rise. Recent advances in coupled climate–ice sheet models provide new opportunities to investigate the role of feedbacks between the ice sheet and the climate system, yet substantial divergence persists across climate-ice sheet model projections. Here, we present results from the Greenland Ice sheet Coupled Model Intercomparison Project (GrICMIP), using three coupled climate–ice sheet models to simulate GrIS evolution under multiple emission scenarios to the year 4000 CE. While projected sea-level contributions remain modest by 2100 (0.03–0.11 m), they diverge strongly on longer timescales, reaching up to 3.5 m by 2500. Under the high-emission scenario, full GrIS disintegration is projected as early as 3000 CE. By means of targeted sensitivity experiments, we identify the dominant sources of diverging GrIS trajectories. Across all models, changes in surface mass balance (SMB), and in particular net surface melt, control the long-term ice-sheet retreat. Differences in SMB formulation, especially in the underlying energy balance models, together with differences in the simulated climate, outweigh the influence of initial ice-sheet geometry. This establishes a hierarchy of uncertainties in which atmospheric processes and their representation within the model systems propagate non-linearly into ice-sheet evolution. Our results demonstrate that reliable long-term projections of the GrIS critically depend on improving the representation of climate and SMB, rather than on refining initial conditions alone.