The first observation of the decay${\mathrm{\Xi }}_b^{-}\to \psi (2S){\mathrm{\Xi }}^{-}$and measurement of the branching ratio of${\mathrm{\Xi }}_b^{-}\to \psi (2S){\mathrm{\Xi }}^{-}$to${\mathrm{\Xi }}_b^{-}\to J/\psi {\mathrm{\Xi }}^{-}$are presented. The$J/\psi$and$\psi (2S)$mesons are reconstructed using their dimuon decay modes. The results are based on proton-proton colliding beam data from the LHC collected by the CMS experiment at$\sqrt{s}=13\mathrm{TeV}$in 2016–2018, corresponding to an integrated luminosity of$140{\mathrm{fb}}^{-1}$. The branching fraction ratio is measured to be$\mathcal{B}({\mathrm{\Xi }}_b^{-}\to \psi (2S){\mathrm{\Xi }}^{-})/\mathcal{B}({\mathrm{\Xi }}_b^{-}\to J/\psi {\mathrm{\Xi }}^{-})=0.84_{-0.19}^{+0.21}(\mathrm{stat})\pm 0.10(\mathrm{syst})\pm 0.02(\mathcal{B})$, where the last uncertainty comes from the uncertainties in the branching fractions of the charmonium states. New measurements of the${\mathrm{\Xi }}_b(5945{)}^0$baryon mass and natural width are also presented, using the${\mathrm{\Xi }}_b^{-}{\pi }^{+}$final state, where the${\mathrm{\Xi }}_b^{-}$baryon is reconstructed through the decays$J/\psi {\mathrm{\Xi }}^{-}$,$\psi (2S){\mathrm{\Xi }}^{-}$,$J/\psi \mathrm{\Lambda }{K}^{-}$, and$J/\psi {\mathrm{\Sigma }}^0{K}^{-}$. Finally, the fraction of${\mathrm{\Xi }}_b^{-}$baryons produced from${\mathrm{\Xi }}_b(5945{)}^0$decays is determined.