The 2012 Indian Ocean earthquake sequence (Mw 8.6, 8.2) is a rare example of great strike-slip earthquakes in an intraoceanic setting. With over a decade of Gravity Recovery and Climate Experiment (GRACE) data, we were able to measure and model the unanticipated large coseismic and postseismic gravity changes of these events. Using the approach of normal mode decomposition and spatial localization, we computed the gravity changes corresponding to five moment tensor components. Our analysis revealed that the gravity changes are produced predominantly by coseismic compression and dilatation within the oceanic crust and upper mantle and by postseismic vertical motion. Our results suggest that the postseismic positive gravity and the postseismic uplift measured with GPS within the coseismic compressional quadrant are best fit by ongoing uplift associated with viscoelastic mantle relaxation. Our study demonstrates that the GRACE data are suitable for analyzing strike-slip earthquakes as small as Mw 8.2 with the noise characteristics of this region.