We present a search for an eV-scale sterile neutrino using 7.5 years of data from the IceCube DeepCore detector. The analysis uses a sample of 21,914 events with energies between 5 and 150 GeV to search for sterile neutrinos through atmospheric muon neutrino disappearance. Improvements in event selection and treatment of systematic uncertainties provide greater statistical power compared to previous DeepCore sterile neutrino searches. Our results are compatible with the absence of mixing between active and sterile neutrino states, and we place constraints on the mixing matrix elements |Uμ4|2<0.0534 and |Uτ4|2<0.0574 at 90% CL under the assumption that Δm412≥1  eV2. These null results add to the growing tension between anomalous appearance results and constraints from disappearance searches in the 3+1 sterile neutrino landscape.