In this article, we report systematic studies of vacancy defects and substitutional defects on the electronic and magnetic properties of HfSe2 monolayer using first-principles calculations. It is found that the monolayer of semiconducting HfSe2 supercell (4 x 4 matrix) becomes metallic on creating a single Se/Hf site vacancy, as well as a pair of vacancies at Hf and Se sites; while it remains semiconducting on creating a Schottky vacancy with an increased band gap value. Magnetic investigations show that a magnetic moment develops on the supercell for single Hf site vacancy and a pair of Hf and Se site vacancies. With a substitutional defect at Hf site by 4d/5d transition metal in monolayer HfSe2, it becomes magnetic with the highest magnetic moment for Tc (4d) and Re (5d) doping. It is noted that monolayer of the HfSe2 supercell becomes half-metallic for Nb, Mo, and W doping. The detailed defect studies of monolayer HfSe2 provide an opportunity for its applications in spintronics.