Polycaprolactone (PCL) is widely used in additive manufacturing for the construction of scaffolds for tissue engineering because of its good bioresorbability, biocompatibility, and processability. Nevertheless, its use is limited by its inadequate mechanical support, slow degradation rate and the lack of bioactivity and ability to induce cell adhesion and, thus, bone tissue regeneration. In this study, we fabricated 3D PCL scaffolds reinforced with a novel Mg-doped bioactive glass (Mg-BG) characterized by good mechanical properties and biological reactivity. An optimization of the printing parameters and scaffold fabrication was performed; furthermore, an extensive microtopography characterization by scanning electron microscopy and atomic force microscopy was carried out. Nano-indentation tests accounted for the mechanical properties of the scaffolds, whereas SBF tests and cytotoxicity tests using human bone-marrow-derived mesenchymal stem cells (BM-MSCs) were performed to evaluate the bioactivity and in vitro viability. Our results showed that a 50/50 wt% of the polymer-to-glass ratio provides scaffolds with a dense and homogeneous distribution of Mg-BG particles at the surface and roughness twice that of pure PCL scaffolds. Compared to pure PCL (hardness H = 35 ± 2 MPa and Young’s elastic modulus E = 0.80 ± 0.05 GPa), the 50/50 wt% formulation showed H = 52 ± 11 MPa and E = 2.0 ± 0.2 GPa, hence, it was close to those of trabecular bone. The high level of biocompatibility, bioactivity, and cell adhesion encourages the use of the composite PCL/Mg-BG scaffolds in promoting cell viability and supporting mechanical loading in the host trabecular bone.