Liquid–liquid phase separation has been shown to underlie the formation and disassembly of membraneless organelles in cells, but the cellular mechanisms that control this phenomenon are poorly understood. A prominent example of regulated and reversible segregation of liquid phases may occur during mitosis, when membraneless organelles disappear upon nuclear-envelope breakdown and reappear as mitosis is completed. Here we show that the dual-specificity kinase DYRK3 acts as a central dissolvase of several types of membraneless organelle during mitosis. DYRK3 kinase activity is essential to prevent the unmixing of the mitotic cytoplasm into aberrant liquid-like hybrid organelles and the over-nucleation of spindle bodies. Our work supports a mechanism in which the dilution of phase-separating proteins during nuclear-envelope breakdown and the DYRK3-dependent degree of their solubility combine to allow cells to dissolve and condense several membraneless organelles during mitosis.