Exploring the unique physical properties of oxide perovskites necessitates their growth on diverse single‐crystal substrates. The thin‐film growth of perovskite SrMnO3 (SMO) has been a particular focus of research due to its emerging room‐temperature multiferroicity. Herein, the epitaxial thin films of (110)‐oriented SMO are grown on the piezoelectric (110)‐oriented (1–x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 (PMN‐PT) substrate. The effects of the thickness and oxygen annealing on the crystal structure, stoichiometry, and ferroelectric properties of the SMO thin film are systematically investigated. The tensile strain produced by the lattice mismatch between the bulk SMO and the PMN‐PT substrate causes an expansion of the c‐lattice parallel to the in‐plane direction of the substrate. The films show larger a‐, b‐, and c‐lattice parameters than the bulk material, resulting in volume expansion of the unit cell. This lattice expansion is attributed to the generation of oxygen vacancies driven by the reduced formation energy caused by the high elastic strain. Piezoelectric force microscopy reveals that the SMO film contains domains with strain‐mediated in‐plane and vacancy‐mediated out‐of‐plane polarization. Furthermore, the piezoelectric response of the PMN‐PT substrate effectively modulates the biaxial tensile strain in the SMO film, offering a potential strategy for controlling the crystal structure and ferroelectric properties of SMO.