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Regulation of electronic structure and mobility cut-on rate in two-dimensional transition metal dichalcogenides (TMDs) has attracted much attention because of its potential in electronic device design. The anisotropic Raman scattering and mobility cut-on rate of monolayer unique distorted-1T(1Td) ReS2 with external strain are determined theoretically based on the density function theory. The angle-dependent Raman spectrum of Ag-like, Eg-like and Cp models are used to discriminate and analysis structural anisotropy; the strain is exploited to adjust the structural symmetry and electronic structure of ReS2 so as to enhance mobility cut-on rate to almost 6 times of the original value. Our results suggest the use of the strain engineering in high-quality semiconductor switch device.