Suffusion refers to a special form of internal erosion characterized by the selective erosion of the finest particles of a soil under the action of an internal fluid flow. In this work, the microscopic mechanism of particle detachment in binary mixtures subjected to suffusion under different flow directions is analyzed. We use the coupled lattice Boltzmann method (LBM) and discrete element method (DEM) to simulate the suffusion process in a granular sample subjected to an anisotropic stress state. When the macro-flow direction is aligned with the principal direction of compression, it is found that the fluid flow is more intense, which increases erosion. The stress anisotropy also influences the detachment direction that is not necessarily correlated with the macroscopic flow direction. The sample’s anisotropic stress state is responsible for directional variations in microstructural properties during the suffusion under different flow directions. From a microscale point of view, a contact sliding index P and a particle detachment index Δ are defined to demonstrate that fluid-induced sliding dominates for particles about to detach.