The recent epitaxial growth of monolayer PtSe2 has raised hope for its novel applications in valleytronic, spintronic, and energy-harvesting devices. Compared with 2H-phase transition-metal dichalcogenides, the 1T-phase PtSe2 is much less studied and this is especially true for its defects behaviors and their influence on electronic properties. In this article, we systemically explore the structure, stability, and kinetics of both Pt and Se vacancies in monolayer PtSe2 using first-principles calculations. By examining the relative energies of these vacancies, we identify the most stable Se/Pt single and double vacancies. In particular, we reveal a new type of Se double vacancy structure with the lowest energy. Energetically, both Se and Pt single vacancies prefer to combine to form double vacancies. All Se and Pt vacancies have remarkable influence on the electronic properties. Moreover, Pt single and double vacancies can introduce strong spin polarization in PtSe2, which may be promising for spintronic applications. These findings not only enrich the fundamental understanding of 1T-phase PtSe2 but also provide useful guidance to design PtSe2 for its optoelectronic and spintronic applications.