Fiber-reinforced polymer (FRP) is widely used in various engineering fields due to its several outstanding properties. In geotechnical engineering, the interactions between FRP and soil play an essential role. In this paper, molecular dynamics (MD) simulation method has been performed to study the interfacial mechanical behavior of epoxy-quartz interface as a subsystem of FRP-soil structure. Uniaxial traction on bulk epoxy was conducted to verify the accuracy of the model. The nanoindentation and nanoscratching mechanisms of epoxy-quartz interface were analyzed, considering the effect of loading rate, sliding velocity, and indentation depth. Abrasion models have been proposed based on the relationship between forces and displacements. Simulation results indicated that the indenter force and the indentation hardness of epoxy substrate increased with the loading rate during nanoindentation, and the relationship between indenter force and indentation depths could be expressed by a power law. The forces along three directions increased with the sliding velocity or indentation depths during nanoscratching, the sliding force and the sliding distance following an exponential function. The numerical simulations demonstrated that the surface wear of the epoxy substrate had the shape of a groove in nanoindentation and a fan-shaped distribution during the nanoscratching process.