  The recent observation of the the gravitational wave event GW170817 and of
its electromagnetic counterpart GRB170817A, from a binary neutron star merger,
has established that the speed of gravitational waves deviates from the speed
of light by less than one part in $10^{15}$. As a consequence, many extensions
of General Relativity are inevitably ruled out. Among these we find the most
relevant sectors of Horndeski gravity. In its original formulation, mimetic
gravity is able to mimic cosmological dark matter, has tensorial perturbations
that travel exactly at the speed of light but has vanishing scalar
perturbations and this fact persists if we combine mimetic with Horndeski
gravity. In this work, we show that implementing the mimetic gravity action
with higher-order terms that break the Horndeski structure yields a
cosmological model that satisfies the constraint on the speed of gravitational
waves and mimics both dark energy and dark matter with a non-vanishing speed of
sound. In this way, we are able to reproduce the $\Lambda$CDM cosmological
model without introducing particle cold dark matter.
