  Decay properties of multi-strangeness $\Xi$ and $\Omega$ baryon resonances
are investigated within the constituent quark model by including relativistic
corrections. The strong decay widths of various $\Xi$ and $\Omega$ resonances
are computed and tested for internal quark configurations to pin down their
spin-parity ($J^P$) quantum numbers and internal structures. We found that the
Roper-like resonances in the multi-strangeness sector have large decay widths
bearing resemblances to their siblings in light and heavy baryon sectors. In
addition, we obtained the decay ratio for the $\Omega(2012)$ as
$\Gamma{(\Omega\to \Xi \bar{K} \pi)} / \Gamma{(\Omega\to \Xi \bar{K})}=4.5\%$,
which is consistent with the experimental data when $J^P=3/2^-$ is assigned.
This observation holds the possibility that the $\Omega(2012)$ could naturally
be explained as a three-quark state in the quark model. The decays of other
low-lying $\Xi$ and $\Omega$ resonances are systematically analyzed, which
would be useful to unveil the structure of these resonances in future
experiments.
