Decays of the ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}$ and ${\mathrm{\ensuremath{\Omega}}}_{b}^{\ensuremath{-}}$ baryons to the charmless final states $p{h}^{\ensuremath{-}}{h}^{\ensuremath{'}\ensuremath{-}}$, where ${h}^{(\ensuremath{'})}$ denotes a kaon or pion, are searched for with the LHCb detector. The analysis is based on a sample of proton-proton collision data collected at center-of-mass energies $\sqrt{s}=7$ and 8 TeV, corresponding to an integrated luminosity of $3\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. The decay ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}$ is observed with a significance of 8.7 standard deviations, and evidence at the level of 3.4 standard deviations is found for the ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay. Results are reported, relative to the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}$ normalization channel, for the products of branching fractions and $b$-hadron production fractions. The branching fractions of ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}$ relative to ${\mathrm{\ensuremath{\Xi}}}_{b}^{\ensuremath{-}}\ensuremath{\rightarrow}p{K}^{\ensuremath{-}}{K}^{\ensuremath{-}}$ decays are also measured.