In this work, we have evaluated the applicability of the so-called thermodynamic scaling and the isomorph frame to describe the shear viscosity of Mie n-6 fluids of varying repulsive exponents (n = 8, 12, 18, 24, and 36). Furthermore, the effectiveness of the thermodynamic scaling to deal with binary mixtures of Mie n-6 fluids has been explored as well. To generate the viscosity database of these fluids, extensive non-equilibrium molecular dynamics simulations have been performed for various thermodynamic conditions. Then, a systematic approach has been used to determine the gamma exponent value (γ) characteristic of the thermodynamic scaling approach for each system. In addition, the applicability of the isomorph theory with a density dependent gamma has been confirmed in pure fluids. In both pure fluids and mixtures, it has been found that the thermodynamic scaling with a constant gamma is sufficient to correlate the viscosity data on a large range of thermodynamic conditions covering liquid and supercritical states as long as the density is not too high. Interestingly, it has been obtained that, in pure fluids, the value of γ is directly proportional to the repulsive exponent of the Mie potential. Finally, it has been found that the value of γ in mixtures can be deduced from those of the pure component using a simple logarithmic mixing rule.