Epitaxial strain may break the orbital degeneracy, favoring a particular orbital filling. This may influence the magnetic properties of transition metal oxides. Herein, we report the consecutive magnetic order and magnetic anisotropy transitions in SrMn0.3Ir0.7O3 (SMIO) thin films, with both 3d and 5d elements on perovskite B sites, as a function of the epitaxial strain. The SMIO films have been epitaxially deposited by pulsed laser deposition on (001)-oriented (LaAlO3)0.3-(Sr2AlTaO6)0.7 substrates buffered with BaTiO3 (BTO) of varying thicknesses. The lattice of the BTO buffer layer relaxes as its thickness increases from 2 to 25 unit cells. Accordingly, the SMIO films deposited epitaxially on top of the BTO buffer layer are subject to a varying strain from compressive to tensile, as the BTO thickness increases, driving the SMIO films from antiferromagnetic to ferromagnetic, and then back to antiferromagnetic, accompanied by a change from perpendicular to in-plane magnetic anisotropy. X-ray linear dichroism spectra reveal that the magnetic order and anisotropy in SMIO are associated with the preferential occupation of the Mn d3z[2]-r[2] or dx[2]-y[2] orbitals, which is controlled in turn by the epitaxial strain.