Perovskite La0.6Sr0.4Fe1−xCuxO3−δ (x = 0, 0.05, 0.1, and 0.2) polycrystalline samples have been synthesized in air and investigated by X‐Ray diffraction, scanning electron microscope, magnetization, and mechanical spectroscopy. An antiferromagnetic transition is observed around 300 K, while no corresponding anomaly is observed in the mechanical spectrum, indicating the absence of conventional magnetoelastic coupling. For La0.6Sr0.4FeO3, an internal friction peak (P1) presents around 140 K and shifts to lower temperatures with increasing Cu‐doping content. Meanwhile, a magnetic anomaly is also observed around P1 peak temperature. As explained, the P1 peak is related to the freezing of the ferroelastic domain walls, and the mechanical energy dissipation is induced by the lagging variation of the octahedral tilting under the alternating stress. This work suggests a peculiar magnetic property of the octahedra within ferroelastic domain walls.