The $\ensuremath{\beta}$-decaying states of $^{70,72}\mathrm{Co}$ were studied at the National Superconducting Cyclotron Laboratory using the VANDLE neutron time-of-flight array. The $({6}^{\ensuremath{-}},{7}^{\ensuremath{-}})\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decaying state in $^{70}\mathrm{Co}$ is near-spherical with a lifetime of $113\ifmmode\pm\else\textpm\fi{}7$ ms, and the low-spin $({1}^{+},{2}^{+})\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decaying state is postulated to be the prolate deformed ground state with a lifetime of $508\ifmmode\pm\else\textpm\fi{}7$ ms. Both decay predominantly to the bound states of $^{70}\mathrm{Ni}$. For the first time neutron-emissions from neutron unbound states from both the $({6}^{\ensuremath{-}},{7}^{\ensuremath{-}})$ and $({1}^{+},{2}^{+})\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ decays were measured. Even with the low statistics data, we were able to disentangle the neutron emission from both decays, which enabled a determination of $\ensuremath{\beta}$-decay strength above the neutron separation energy of $^{70}\mathrm{Ni}$. Neutron emission probabilities were measured to be $7.1\ifmmode\pm\else\textpm\fi{}1.5%$ and $9.4\ifmmode\pm\else\textpm\fi{}1.7%$, respectively, for the $({6}^{\ensuremath{-}},{7}^{\ensuremath{-}})$ and $({1}^{+},{2}^{+})$ decays. The decay pattern of the $^{70}\mathrm{Co}$ is driven by neutron ${f}_{5/2}$ to proton ${f}_{7/2}$ Gamow-Teller transformation. The observed population of neutron unbound states is attributed to the conversion of ${p}_{1/2}$ and ${p}_{3/2}$ neutrons to ${p}_{3/2}$ and ${p}_{1/2}$ protons excited across the $Z=28$ closed shell.
