In this study, biomimetic borate-based bioactive glass scaffolds containing hexagonal boron nitride hBN nanoparticles (0.1, 0.2, 0.5, 1, and 2% by weight) were manufactured with the polymer foam replication technique to be used in hard tissue engineering and drug delivery applications. To create three-dimensional cylindrical-shaped scaffolds, polyurethane foams were used as templates and covered using a suspension of glass and hBN powder mixture. Then, a heat treatment was applied at 570 °C in an air atmosphere to remove the polymer foam from the structure and to sinter the glass structures. The structural, morphological, and mechanical properties of the fabricated composites were examined in detail. The in vitro bioactivity of the prepared composites was tested in simulated body fluid, and the release behavior of gentamicin sulfate and 5-fluorouracil from glass scaffolds were analyzed separately as a function of time. The cytotoxicity was investigated using osteoblastic MC3T3-E1 cells. The findings indicated that the hBN nanoparticles, up to a certain concentration in the glass matrix, improved the mechanical strength of the glass scaffolds, which mimic the cancellous bone. Additionally, the inclusion of hBN nanoparticles enhanced the in vitro hydroxyapatite-forming ability of bioactive glass composites. The presence of hBN nanoparticles accelerated the drug release rates of the system. It was concluded that bioactive glass/hBN composite scaffolds mimicking native bone tissue could be used for bone tissue repair and regeneration applications.