We use first-principles free-energy calculations to predict a pressure-induced spin crossover in the liquid planetary material (Mg,Fe)O, whereby the magnetic moments of Fe ions vanish gradually over a range of hundreds of GPa. Because electronic entropy strongly favors the nonmagnetic low-spin state of Fe, the crossover has a negative effective Clapeyron slope, in stark contrast to the crystalline counterpart of this transition-metal oxide. Diffusivity of liquid (Mg,Fe)O is similar to that of MgO, displaying a weak dependence on element and spin state. Fe-O and Mg-O coordination increases from approximately 4 to 7 as pressure goes from 0 to 200 GPa. We find partitioning of Fe to induce a density inversion between the crystal and melt, implying separation of a basal magma ocean from a surficial one in the early Earth. The spin crossover induces an anomaly into the density contrast, and the oppositely signed Clapeyron slopes for the crossover in the liquid and crystalline phases imply that the solid-liquid transition induces a spin transition in (Mg,Fe)O.