We use Mars Atmosphere and Volatile EvolutioN observations of the upstream solar wind, and Mars Express observations of ionospheric electron densities and magnetic fields, to study how the topside ionosphere (>320 km) of Mars is affected by variations in solar wind dynamic pressure. We find that high solar wind dynamic pressures result in the topside ionosphere being depleted of plasma at all solar zenith angles, coincident with increased induced magnetic field strengths. The depletion of topside plasma in response to high solar wind dynamic pressures is observed in both weak and strong crustal magnetic field regions. Taken together, our results suggest that high solar wind dynamic pressures lead to ionospheric compression, increased ion escape, and reduced day-to-night plasma transport in the high-altitude nightside ionosphere. Plain Language Summary Mars lacks a global dipole magnetic field to hold off the solar wind. As a consequence, the solar wind can significantly affect the structure of the topside ionosphere. Previous studies detailing these effects, however, have primarily focused on impulsive space weather events. In this work, we use observations from two spacecraft (MAVEN and Mars Express) to statistically study how the solar wind dynamic pressure affects the topside ionosphere. We find that, during times of high solar wind dynamic pressure, the ionosphere is globally depleted of plasma, which suggests that the ionosphere is compressed and plasma escape is enhanced.