  Let $X \hookrightarrow \overline{X}$ be an open immersion of smooth varieties
over a field of characteristic $p>0$ such that the complement is a simple
normal crossing divisor and let $\overline{Z} \subseteq Z \subseteq
\overline{X}$ be closed subschemes of codimension at least $2$. In this paper,
we prove that the canonical restriction functor between the category of
overconvergent $F$-isocrystals $F\text{-}{\rm Isoc}^{\dagger}(X,\overline{X})
\longrightarrow F\text{-}{\rm Isoc}^{\dagger}(X \setminus Z, \overline{X}
\setminus \overline{Z})$ is an equivalence of categories. We also prove an
application to the category of $p$-adic representations of the fundamental
group of $X$, which is a higher-dimensional version of a result of Tsuzuki.
