We study the cosmic aspects of the evolving universe by taking into account mimetic gravity. Mimetic gravity is a Weyl-symmetric expansion of general relativity linked by a single disformal transformation, in which the presence of a dust-like perfect fluid may be used to imitate cold dark matter on a cosmic scale. We consider three well-known equation of state (EoS) parameterizations in terms of redshift function, z. Using mimetic gravity energy density, we calculate the potential V, coincidence parameter r and deceleration parameter q for all parametrization models with the help of energy conservation equation, Lagrange multiplier and normalized Hubble parameter. Considering the observational values of parameters in parametrization models, we get some useful results for the underlying scenario. Additionally we attempt a numerical reconstruction of the potential V as a function of the mimetic scalar field ϕ.