In nova outbursts on oxygen-neon white dwarfs, the $^{30}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{31}\mathrm{S}$ reaction plays a crucial role in the synthesis of heavier nuclear species, from Si to Ca. However, this important rate is very uncertain as a result of the lack of spectroscopic information on most of the levels above the proton threshold in $^{31}\mathrm{S}$. To reduce these uncertainties, we have measured differential cross sections for the $^{32}\mathrm{S}$($p,d$)$^{31}\mathrm{S}$ reaction and determined excitation energies for states in $^{31}\mathrm{S}$. A total of 26 states in $^{31}\mathrm{S}$ were observed, including 17 above the proton threshold. Five new states were observed. Spins and parities were determined or constrained for 15 of the observed levels through a distorted wave Born approximation analysis of the angular distributions, of which six were made for the first time. We have evaluated 66 levels using existing data in combination with this measurement and calculated a new $^{30}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{31}\mathrm{S}$ reaction rate. We confirmed the spin-parity assignment of ${1/2}^{+}$ for the state at 6263 keV which dominates the $^{30}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{31}\mathrm{S}$ reaction rate at lower temperatures in novae, while the state at 6544 keV dominates at temperatures above 0.2 GK. Our results indicate that the $^{30}\mathrm{P}$($p,\ensuremath{\gamma}$)$^{31}\mathrm{S}$ rate is reduced by up to a factor of 10 at nova temperatures compared to previous estimates.