Data from three experiments using the heavy-ion fusion evaporation-reaction ${}^{36}\mathrm{Ar}+{}^{28}\mathrm{Si}$ have been combined to study high-spin states in the residual nucleus $^{60}\mathrm{Ni}$, which is populated via the evaporation of four protons from the compound nucleus $^{64}\mathrm{Ge}$. The GAMMASPHERE array was used for all the experiments in conjunction with a $4\ensuremath{\pi}$ charged-particle detector arrays (MICROBALL, LUWUSIA) and neutron detectors (NEUTRON SHELL) to allow for the detection of $\ensuremath{\gamma}$ rays in coincidence with the evaporated particles. An extended $^{60}\mathrm{Ni}$ level scheme is presented, comprising more than $270\ensuremath{\gamma}$-ray transitions and 110 excited states. Their spins and parities have been assigned via directional correlations of $\ensuremath{\gamma}$ rays emitted from oriented states. Spherical shell-model calculations in the $\mathit{fp}$-shell characterize some of the low-spin states, while the experimental results of the rotational bands are analyzed with configuration-dependent cranked Nilsson-Strutinsky calculations.