This work reports on numerical characterizations of effective mechanical properties associated with graphene-polymer composite aerogels produced using an environmentally friendly freeze-drying process. To this purpose, a multiscale approach was implemented, in which geometrical configurations were constructed based on the results of experimental characterizations. A homogenization procedure based on molecular mechanics, the Milton method, and the asymptotic homogenization method was applied. In the asymptotic homogenization method, cell problems were formulated and solved within a representative volume element using the finite element method. After validating the numerical model through experimental results from compression tests, a parametric study on the influence of microstructural parameters of the materials, such as dispersion state, aspect ratio, volume fraction of nanoinclusions, and material porosity, on the macroscopic mechanical behavior of the composite aerogels was conducted. The simulation results provided a deeper understanding of the mechanisms that enhanced the mechanical properties of such aerogels by adding various graphene derivatives, allowing for adjustments in the elaboration process to obtain materials with improved mechanical properties.