Novel bioactive glasses based on a Ca- and Mg-modified silicon oxycarbide (SiCaMgOC) were prepared from a polymeric single-source precursor, and their in vitro activity towards hydroxyapatite mineralization was investigated upon incubating the samples in simulated body fluid (SBF) at 37 °C. The as-prepared materials exhibit an outstanding resistance against devitrification processes and maintain their amorphous nature even after exposure to 1300 °C. The X-ray diffraction (XRD) analysis of the SiCaMgOC samples after the SBF test showed characteristic reflections of apatite after only three days, indicating a promising bioactivity. The release kinetics of the Ca2+ and Mg2+ and the adsorption of H+ after immersion of SiCaMgOC in simulated body fluid for different soaking times were analyzed via optical emission spectroscopy. The results show that the mechanism of formation of apatite on the surface of the SiCaMgOC powders is similar to that observed for standard (silicate) bioactive glasses. A preliminary cytotoxicity investigation of the SiOC-based bioactive glasses was performed in the presence of mouse embryonic fibroblasts (MEF) as well as human embryonic kidney cells (HEK-293). Due to their excellent high-temperature crystallization resistance in addition to bioactivity, the Ca- and Mg-modified SiOC glasses presented here might have high potential in applications related to bone repair and regeneration.