  In this brief note we investigate the conditions under which a Schwarzschild
de Sitter black hole spacetime is a solution of the mimetic $F(R)$ gravity with
Lagrange multiplier and potential. As we demonstrate, the resulting mimetic
$F(R)$ gravity is a slight modification of the ordinary $F(R)$ gravity case,
however the resulting perturbation equations are not in all cases identical to
the ordinary $F(R)$ gravity case. In the latter case, the perturbation
equations are identical to the ones corresponding to the Reissner-Nordstr\"{o}m
anti-de Sitter black hole.
