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The dielectric properties of non-stoichiometric SrMnO₃ (SMO) thin films grown by molecular beam epitaxy were systematically investigated. Especially, the effects of cation stoichiometry-induced diverse types and densities of defects on the dielectric properties of SMO films were revealed. Two anomalous dielectric relaxation behaviors were observed at different temperatures in both Sr-rich and Mn-rich samples. High-temperature dielectric relaxation, resulting from a short-range Mn-related Jahn–Teller (JT) polaron hopping motion, was reinforced by an enhancement of JT polaron density in the Sr-rich film, which contained abundant SrO Ruddlesden–Popper (R-P) stacking faults. However, an excessive number of disordered Sr vacancy clusters in Mn-rich thin film suppressed the hopping path of JT polarons and enormously weakened this dielectric relaxation. Thus, The Sr-rich film demonstrated a higher dielectric constant and dielectric loss than the Mn-rich film. In addition, low-temperature dielectric relaxation may be attributed to the polarization/charge glass state.