Abstract We introduce FloeNet, a graph neural network trained to emulate the Geophysical Fluid Dynamics Laboratory global sea ice model, SIS2. FloeNet is a mass‐conserving model, emulating 6‐hr mass and area budget tendencies related to sea ice and snow‐on‐sea‐ice growth, melt, and advection. We train FloeNet using SIS2 data from a reanalysis‐forced ice‐ocean simulation and test its ability to generalize to pre‐industrial and 1% CO2 forcing conditions. FloeNet outperforms a non‐conservative model at reproducing sea ice and snow‐on‐sea‐ice mean state, trends, and inter‐annual variability, with volume anomaly correlations above 0.96 in the Antarctic and 0.76 in the Arctic, across all forcings. FloeNet also produces the correct thermodynamic‐dynamic response to forcing, enabling physical interpretability of emulator output. Finally, we show that FloeNet outputs high‐fidelity coupling‐related variables, including ice‐surface temperature, ice‐to‐ocean salt flux, and melting energy fluxes. We hypothesize that FloeNet will improve polar climate processes within existing atmosphere and ocean emulators.