Breakdown of Schmid's law is a long-standing problem for exploring the orientation-dependent deformation mechanism in intermetallics. The lack of atomic-level understanding of the selection rules for the plastic deformation modes has seriously limited designing strong and ductile intermetallics for high-temperature applications. Here we put forward a transparent model solely based on first principles simulations for mapping the deformation modes in γ-TiAl polysynthetic twinned alloys. The model bridges intrinsic energy barriers and different deformation mechanisms and beautifully resolves the complexity of the observed orientation-dependent deformation mechanisms. Using the model, one can elegantly reveal the atomic-level mechanisms behind the unique channeled flow phenomenon in lamellar TiAl alloys.