The use of three-dimensional (3D) scaffolds is recognized worldwide as a valuable biomedical approach for promoting tissue regeneration in critical-size bone defects. Over the last 50 years, bioactive glasses have been intensively investigated in a wide range of different clinical applications, from orthopedics to soft tissue healing. Bioactive glasses exhibit the unique capability to chemically bond to the host tissue and, furthermore, their processing versatility makes them very appealing due to the availability of different manufacturing techniques for the production of porous and interconnected synthetic bone grafts able to support new tissue growth over the whole duration of the treatment. As a novel contribution to the broad field of scaffold manufacturing, we report here an effective and relatively easy method to produce silicate glass-derived scaffolds by using, for the first time in the biomedical field, dolomite powder as a foaming agent for the formation of 3D bone-like porous structures. Morphological/structural features, crystallization behavior, and in vitro bioactivity in a simulated body fluid (SBF) were investigated. All the tested scaffolds were found to fulfil the minimum requirements that a scaffold for osseous repair should exhibit, including porosity (65–83 vol.%) and compressive strength (1.3–3.9 MPa) comparable to those of cancellous bone, as well as hydroxyapatite-forming ability (bioactivity). This study proves the suitability of a dolomite-foaming method for the production of potentially suitable bone grafts based on bioactive glass systems.