Bone tissue engineering has been developed in the past decades, with the engineering of bone substitutes on the vanguard of this regenerative approach. Polycaprolactone-based scaffolds are fairly applied for bone regeneration, and several composites have been incorporated so as to improve the scaffolds’ mechanical properties and tissue in-growth. In this study, hydroxyapatite is incorporated on polycaprolactone-based scaffolds at two different proportions, 80:20 and 60:40. Scaffolds are produced with two different blending methods, solvent casting and melt blending. The prepared composites are 3D printed through an extrusion-based technique and further investigated with regard to their chemical, thermal, morphological, and mechanical characteristics. In vitro cytocompatibility and osteogenic differentiation was also assessed with human dental pulp stem/stromal cells. The results show the melt-blending-derived scaffolds to present more promising mechanical properties, along with the incorporation of hydroxyapatite. The latter is also related to an increase in osteogenic activity and promotion. Overall, this study suggests polycaprolactone/hydroxyapatite scaffolds to be promising candidates for bone tissue engineering, particularly when produced by the MB method.