  In this paper, a notion of cyclotomic (or level $k$) walled Brauer algebras
$\mathscr B_{k, r, t}$ is introduced for arbitrary positive integer $k$. It is
proven that $\mathscr B_{k, r, t}$ is free over a commutative ring with rank
$k^{r+t}(r+t)!$ if and only if it is admissible. Using super Schur-Weyl duality
between general linear Lie superalgebras $\mathfrak{gl}_{m|n}$ and $\mathscr
B_{2, r, t}$, we give a classification of highest weight vectors of
$\mathfrak{gl}_{m|n}$-modules $M_{pq}^{rt}$, the tensor products of Kac-modules
with mixed tensor products of the natural module and its dual. This enables us
to establish an explicit relationship between $\mathfrak{gl}_{m|n}$-Kac-modules
and right cell (or standard) $\mathscr B_{2, r, t}$-modules over $\mathbb C$.
Further, we find an explicit relationship between indecomposable tilting
$\mathfrak{gl}_{m|n}$-modules appearing in $M_{pq}^{rt}$, and principal
indecomposable right $\mathscr B_{2, r, t}$-modules via the notion of Kleshchev
bipartitions. As an application, decomposition numbers of $\mathscr B_{2, r,
t}$ arising from super Schur-Weyl duality are determined.
