The alveolar bone is a unique type of bone, and the goal of bone tissue engineering (BTE) is to develop methods to facilitate its regeneration. Currently, an emerging trend involves the fabrication of polycaprolactone (PCL)-based scaffolds using a three-dimensional (3D) printing technique to enhance an osteoconductive architecture. These scaffolds are further modified with hydroxyapatite (HA), type I collagen (CGI), or chitosan (CS) to impart high osteoinductive potential. In conjunction with cell therapy, these scaffolds may serve as an appealing alternative to bone autografts. This review discusses research gaps in the designing of 3D-printed PCL-based scaffolds from a biomimetic perspective. The article begins with a systematic analysis of biological mineralisation (biomineralisation) and ossification to optimise the scaffold's structural, mechanical, degradation, and surface properties. This scaffold-designing strategy lays the groundwork for developing a research pathway that spans fundamental principles such as molecular dynamics (MD) simulations and fabrication techniques. Ultimately, this paves the way for systematic in vitro and in vivo studies, leading to potential clinical applications.