  The hadron-deuteron correlation function has attracted many interests as a
potential method to access the three-hadron interactions. However, the
weakly-bound nature of deuteron has not been considered in the preceding
studies. In this study, the breakup effect of deuteron on the deuteron-$\Xi^-$
($d$-$\Xi^-$) correlation function $C_{d\Xi^-}$ is investigated. The
$d$-$\Xi^-$ scattering is described by a nucleon-nucleon-$\Xi$ three-body
reaction model. The continuum-discretized coupled-channels method, which is a
fully quantum-mechanical and non-perturbative reaction model, is adopted.
$C_{d\Xi^-}$ turns out to be sensitive to the strong interaction and enhanced
by the deuteron breakup effect by 6--8~\% for the $d$-$\Xi^-$ relative momentum
below about 70 MeV/$c$. Low-lying neutron-neutron continuum states are
responsible for this enhancement. Within the adopted model, the deuteron
breakup effect on $C_{d\Xi^-}$ is found to be appreciable but not very
significant. Except for the enhancement by several percent, studies on
$C_{d\Xi^-}$ without the deuteron breakup effect can be justified.
