Excited states in the neutron-rich isotopes $^{57\ensuremath{-}60}\mathrm{Mn}$ have been studied with fusion-evaporation reactions induced by $^{48}\mathrm{Ca}$ beams at $130$ MeV on $^{13,14}\mathrm{C}$ targets. Level schemes have been deduced reaching spins of $~16\ensuremath{\hbar}$ and $~27\ensuremath{\hbar}/2$ in the odd-odd and odd-even isotopes, respectively. States with natural parity within an $\mathit{fp}$ model space are compared to the predictions of large-scale shell-model calculations using the recently developed GXPF1A effective interaction. Quasirotational structures are evident in all of the isotopes and are discussed in terms of the deformation-driving potential of the $\ensuremath{\nu}1{g}_{9/2}$ intruder orbital. It is apparent that an enlarged model space, incorporating at least the $1{g}_{9/2}$ intruder state, is necessary to reproduce the observed experimental systematics in a more satisfactory manner.