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 $C_{dXi^-}$ 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. $C_{dXi^-}$ 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 $C_{dXi^-}$ is found to be appreciable but not very significant. Except for the enhancement by several percent, studies on $C_{dXi^-}$ without the deuteron breakup effect can be justified.
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