  On the 17th of August 2017, the thriving discovery of gravitational waves
event GW170817 and its optical counterpart GRB170817A, owing to coalescing of
two neutron starts divulged a very small amount of difference around ${\cal
O}(10^{-16})$ between traveling speed of light and the velocity of
gravitational waves ($C_{T}$). This small deviation can be used as a strong
constraint on modified gravity models. We concentrate on the Higher-Order
expansion of Mimetic Gravity (HOMimG) model to specify the parametric space of
three parameters of our model ($a$, $b$, and $c$ ) utilizing the observational
constraint from GW170817-GRB170817A on $C_{T}$, besides two theoretical
constraints on $C_{T}^{2}$ and $C_{s}^{2}$ due to assurance of the stability of
the model and subluminal promulgation of the scalar and tensor perturbations.
Thereafter, we increase the accuracy of the parametric space with the aid of
imposing further limitation of $\gamma$ parameter (related to the age of the
Universe). In pursuance of determining the other parameter of the model
($\lambda$), the potential of the model is specified, and another observational
bound related to the Equation of State (EoS) parameter of dark energy is taken
into account. In consequence, we attain a viable HOMimG model confined to
numbers of observational and theoretical constraints. At the end, regarding the
concluded numerical ranges for the model parameters, and cogitating two
different potential (quadratic and quartic potentials) to specify $\lambda$
parameter, we illustrate that the values of the model parameters are
independent of the form of potential.
