In this study, three-dimensional (3D) magnetic Fe3O4 nanoparticles containing mesoporous bioactive glass/polycaprolactone (Fe3O4/MBG/PCL) composite scaffolds have been fabricated by the 3D-printing technique. The physiochemical properties, in vitro bioactivity, anticancer drug delivery, mechanical strength, magnetic heating ability and cell response of Fe3O4/MBG/PCL scaffolds were systematically investigated. The results showed that Fe3O4/MBG/PCL scaffolds had uniform macropores of 400 μm, high porosity of 60% and excellent compressive strength of 13–16 MPa. The incorporation of magnetic Fe3O4 nanoparticles into MBG/PCL scaffolds did not influence their apatite mineralization ability but endowed excellent magnetic heating ability and significantly stimulated proliferation, alkaline phosphatase (ALP) activity, osteogenesis-related gene expression (RUNX2, OCN, BSP, BMP-2 and Col-1) and extra-cellular matrix (ECM) mineralization of human bone marrow-derived mesenchymal stem cells (h-BMSCs). Moreover, using doxorubicin (DOX) as a model anticancer drug, Fe3O4/MBG/PCL scaffolds exhibited a sustained drug release for use in local drug delivery therapy. Therefore, the 3D-printed Fe3O4/MBG/PCL scaffolds showed the potential multifunctionality of enhanced osteogenic activity, local anticancer drug delivery and magnetic hyperthermia.