Strong two- and three-body decays of the new excited hyperon $Omega^*(2012)$ are discussed in the hadronic molecular approach. The $Omega^*(2012)$ state is considered to contain the mixed $Xi bar K$ and $Omega eta$ hadronic components. In our calculations we use a phenomenological hadronic Lagrangian describing the coupling of the bound states to its constituents and of the constituents to other hadrons occurring in the final state. Our results show that the decay widths of the two-body decay modes $Omega^*(2012) to Xi bar K$ lie in the few MeV region and are compatible with or dominate over the rates of the three-body modes $Omega^*(2012) to Xi pi bar K$. The sum of two- and three-body decay widths is consistent with a width of the $Omega^*(2012)$ originally measured by the Belle Collaboration. A possible scenario for the suppression of the three-body decay rate recently noticed by the Belle Collaboration is due to the dominant admixture of the $Omega eta$ hadronic component in the $Omega^*(2012)$ state.