  In this paper, we study the structure and gravitational resonances of thick
branes generated by a mimetic scalar field in $f(R)$ gravity. We obtain several
typical thick brane solutions for $f(R)=R+\alpha R^2$. To study their
stability, we analyze the tensor perturbation of the metric. It is shown that
any thick brane model with $df/dR>0$ is stable and the graviton zero mode can
be localized on the brane for each solution, which indicates that the
four-dimensional Newtonian gravity can be restored. The effect of the parameter
$\alpha$ on the gravitational resonances is studied. As a brane splits into
multi sub-branes, the effective potential of the tensor perturbation will have
an abundant inner structure with multi-wells, and this will lead to new
phenomena of the gravitational resonances.
