Mitotic spindles assemble in a crowded cytoplasm whose physical properties can change during functional transitions between cell states. How cytoplasmic properties influence spindle architecture and scaling remains unknown. Spindle scaling relationships have been described in early animal development when cell volumes reduce dramatically. However, cells in these early developmental stages are transcriptionally inactive and rely on the cytoplasmic composition of the fertilised egg. By contrast, it is unknown whether and how differentiating cells in later stages of development adjust spindle architecture, specifically during brain development when spindle defects have severe pathological consequences. Using automated, non-invasive microscopy and three-dimensional analyses, we show concerted changes in cell and spindle morphology of murine embryonic stem cells undergoing neural differentiation. Remarkably, while tubulin biochemistry and microtubule dynamics remain unchanged, spindles in early-differentiated cells are smaller than spindles in equally-sized undifferentiated stem cells. Using quantitative theory and biophysical perturbations in combination with optical diffraction tomography, we find that differentiation-driven cytoplasmic dilution and a decrease in free tubulin concentration drive a CPAP-dependent increase in centrosomal nucleation capacity. As a consequence, in early-differentiated cells, microtubule mass is redistributed towards the spindle poles at the expense of the spindle bulk. For the first time, our study links cell-type specific cytoplasmiclle material properties to mitotic organelle morphology and scaling.