Understanding the mechano–biological coupling mechanisms of biomaterials for tissue engineering is of major importance to assure proper scaffold performance in situ. Therefore, it is of paramount importance to establish correlations between biomaterials, their processing conditions, and their mechanical behaviour, as well as their biological performance. With this work, it was possible to infer a correlation between the addition of graphene nanoparticles (GPN) in a concentration of 0.25, 0.5, and 0.75% (w/w) (GPN0.25, GPN0.5, and GPN0.75, respectively) in three-dimensional poly(ε-caprolactone) (PCL)-based scaffolds, the extrusion-based processing parameters, and the lamellar crystal orientation through small-angle X-ray scattering experiments of extruded samples of PCL and PCL/GPN. Results revealed a significant impact on the scaffold’s mechanical properties to a maximum of 0.5% of GPN content, with a significant improvement in the compressive modulus of 59 MPa to 93 MPa. In vitro cell culture experiments showed the scaffold’s ability to support the adhesion and proliferation of L929 fibroblasts (fold increase of 28, 22, 23, and 13 at day 13 (in relation to day 1) for PCL, GPN0.25, GPN0.5, and GPN0.75, respectively) and bone marrow mesenchymal stem/stromal cells (seven-fold increase for all sample groups at day 21 in relation to day 1). Moreover, the cells maintained high viability, regular morphology, and migration capacity in all the different experimental groups, assuring the potential of PCL/GPN scaffolds for tissue engineering (TE) applications.