  In mimetic gravity, we derive $D$-dimension charged black hole solutions
having flat or cylindrical horizons with zero curvature boundary. The
asymptotic behaviours of these black holes behave as (A)dS. We study both
linear and nonlinear forms of the Maxwell field equations in two separate
contexts. For the nonlinear case, we derive a new solution having a metric with
monopole, dipole and quadrupole terms. The most interesting feature of this
black hole is that its dipole and quadruple terms are related by a constant.
However, the solution reduces to the linear case of the Maxwell field equations
when this constant acquires a null value. Also, we apply a coordinate
transformation and derive rotating black hole solutions (for both linear and
nonlinear cases). We show that the nonlinear black hole has stronger curvature
singularities than the corresponding known black hole solutions in general
relativity. We show that the obtained solutions could have at most two
horizons. We determine the critical mass of the degenerate horizon at which the
two horizons coincide. We study the thermodynamical stability of the solutions.
We note that the nonlinear electrodynamics contributes to process a
second-order phase transition whereas the heat capacity has an infinite
discontinuity.
