We report a spin reorientation from Γ4(Gx, Ay, Fz) to Γ1(Ax, Gy, Cz) magnetic configuration near room temperature and a re-entrant transition from Γ1(Ax, Gy, Cz) to Γ4(Gx, Ay, Fz) at low temperature in TbFe1-xMnxO3 single crystals by performing both magnetization and neutron diffraction measurements. The Γ4 - Γ1 spin reorientation temperature can be enhanced to room temperature when x is around 0.5 ~ 0.6. These new transitions are distinct from the well-known Γ4 - Γ2 transition observed in TbFeO3, and the sinusoidal antiferromagnetism to complex spiral magnetism transition observed in multiferroic TbMnO3. We further study the evolution of magnetic entropy change (-ΔSM) versus Mn concentration to reveal the mechanism of the re-entrant spin reorientation behavior and the complex magnetic phase at low temperature. The variation of -ΔSM between a and c axes indicates the significant change of magnetocrystalline anisotropy energy in the TbFe1-xMnxO3 system. Furthermore, as Jahn-Teller inactive Fe(3+) ions coexist with Jahn-Teller active Mn(3+) ions, various anisotropy interactions, compete with each other, giving rise to a rich magnetic phase diagram. The large magnetocaloric effect reveals that the studied material could be a potential magnetic refrigerant. These findings expand our knowledge of spin reorientation phenomena and offer the alternative realization of spin-switching devices at room temperature in the rare-earth orthoferrites.