The thermodynamic, structural, magnetic and electronic properties of the pristine and intrinsic vacancy-defect-containing topological Dirac semimetal Ba3SnO are studied using first-principles density functional theory calculations. The thermodynamic stability of Ba3SnO has been evaluated with reference to its competing binary phases Ba2Sn, BaSn and BaO. Subsequently, valid limits of the atomic chemical potentials derived from the thermodynamic stability were used for assessing the formation of Ba, Sn and O vacancy defects in Ba3SnO under different synthesis environments. Based on the calculated defect-formation energies, we find that the charge-neutral oxygen vacancies are the most favourable type of vacancy defect under most chemical environments. The calculated electronic properties of pristine Ba3SnO show that inclusion of spin-orbit coupling in exchange-correlation potentials computed using generalized gradient approximation yields a semimetallic band structure exhibiting twin Dirac cones along the Γ-X path of the Brillouin zone. The effect of spin-polarization and spin-orbit coupling on the physical properties of intrinsic vacancy defects containing Ba3SnO has been examined in detail. Using Bader charges, electron localization function (ELF), electronic density of states (DOS) and spin density, we show that the isolated oxygen vacancy is a magnetic defect in anti-perovskite Ba3SnO. Our results show that the origin of magnetism in Ba3SnO is the accumulation of unpaired charges at the oxygen vacancy sites, which couple strongly with the 5d states of the Ba atom. Owing to the metastability observed in earlier theoretically predicted magnetic topological semimetals, the present study reveals the important role of intrinsic vacancy defects in giving rise to magnetism and also provides opportunities for engineering the electronic structure of a Dirac semimetal.