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Triple-layered Sr₄Ru₃O₁₀ is a unique ferromagnetic system with the central RuO₆ layer behaving differently from two outer layers both crystallographically and magnetically. We report that the partial substitution of Ru by smaller Mn gives rise to modifications in crystal structure, and electronic and magnetic properties of Sr₄(Ru_1-xMn_x)₃O₁₀. Through the single crystal x-ray diffraction refinement, we find that (Ru/Mn)O₆ octahedral rotation is reduced with increasing x and becomes undetectable at x ≥ 0.23, making the system changing from the orthorhombic to tetragonal structure. The magnetization measurement indicates the ferromagnetic transition temperature T_C decreases from 105 K (x = 0) to 70 K for x = 0.41, with the reduced average magnetic moment as well. What is remarkable is that Mn doping induces magnetic anisotropy change from the easy c axis in x = 0 to the easy ab plane in x = 0.41. Such change also removes the ab-plane metamagnetic transition observed in x = 0. Furthermore, the electrical resistivity increases with increasing x showing semiconducting behavior for x = 0.41. We discuss our results in the context of strong spin-charge-lattice-orbital interaction.