  We analyze the role of the left-left squark mixing in the rare $K^+
\rightarrow \pi^+\nu\bar{\nu}$ decay within the minimal supersymmetry with a
large $\tan\beta$. A Higgs boson mass of 125 GeV has been taken into account
leading to correlation between stop masses and trilinear soft supersymmetry
breaking coupling $A_{\tilde{t}}$. We find that measurable effects, similar to
that of the well known $LR$ squark mixing terms, are possible for large
$A_{\tilde{t}}$ combined with the off-diagonal $LL$-insertions. Precise
measurements of the decay rate are expected from the ongoing NA62 experiment at
CERN. We emphasize that the effect we present can put certain limits on the
left-left flavor changing structure of the squark mass matrix.
