  The vacuum, static, and spherically symmetric solutions in the mimetic
Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a
reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the
mimetic approach. Due to the mimetic field, the theory contains non-trivial
vacuum solutions different from those in Einstein gravity. We find that with
the existence of the mimetic field, the spacelike singularity inside a
Schwarzschild black hole could be altered to a lightlike singularity, even
though the curvature invariants still diverge at the singularity. Furthermore,
in this case, the maximal proper time for a timelike radially-infalling
observer to reach the singularity is found to be infinite.
