The $Z$-boson decay provides good opportunity in searching for $\Xi_{bQ}$ baryon due to the large quantity of its events can be collected at high energy colliders. In this paper, we performed a complete investigation of the indirect production of the $\Xi_{bc}$ and $\Xi_{bb}$ baryon via $Z$-boson decay processes $Z\to \Xi_{bQ}+\bar b +\bar Q$ with $Q= (c,b)$ quark under NRQCD factorization approach. After considering the contribution from the diquark states $\langle bc\rangle[^3S_1]_{\bar 3/6}$, $\langle bc\rangle[^1S_0]_{\bar 3/6}$, $\langle bb\rangle [^1S_0]_6$ and $\langle bb\rangle[^3S_1]_{\bar 3}$, the calculated branching fractions are ${\cal B}(Z\to\Xi_{bc}+X) = 3.595\times 10^{-5}$ and ${\cal B}(Z\to\Xi_{bb}+X) = 1.213\times 10^{-6}$. Forthermore, the $\Xi_{bc}$ and $\Xi_{bb}$ production events are predicted to be at the $10^4$ and $10^3$ order level on the LHC collider, $10^7$ and $10^6$ order level for the CEPC collider. Finally, we have estimated the production ratio for $Z\to c\bar c(b\bar b)\to\Xi^{+,0}_{bc}+X $ with $\Xi^{+,0}_{bc} \to \Lambda^+_c$ in $Z$-boson decay, i.e. ${\cal R}(Z\to c\bar c\to\Xi^{+,0}_{bc}+X) \sim {\cal O}(10^{-6})$ and ${\cal R}(Z\to b\bar b\to\Xi^{+,0}_{bc}+X) \sim {\cal O}(10^{-5})$, respectively. Finally, we present the differential decay widths of $\Xi_{bc}$ and $\Xi_{bb}$ with respect to $s_{23}$ and $z$ distributions, and analyze the uncertainties. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.