This study employs two-temperature molecular dynamics simulations to investigate swift heavy ion irradiation of SiO2 substrate-supported two-dimensional material graphene. Material-dependent electronic and thermal properties are integrated into each region to model the energy transfer between the electronic and atomic subsystems of the studied materials. Simulations of interactions with Xe heavy ions are performed with ion kinetic energies ranging from 0.5 to 25 GeV with electronic stopping powers from ∼2.6 to 17.7 keV/nm. With the studied ion energy range, nanopores with a diameter of up to 5 nm can be formed in graphene due to the thermally driven sputtering effect, while amorphization occurs along the ion track in the SiO2 substrate. The coupling between the substrate and two-dimensional material significantly impacts the structural change due to heat transfer and atomic interactions among different layers of materials. The method applied in this work provides a valuable tool for modeling and understanding the structural modifications induced by ion irradiation in layered structures.