Cell-permeable small molecules that inhibit their targets on fast timescales are powerful probes of cell-division mechanisms. Such inhibitors have been identified using phenotype-based screens with chemical libraries. However, the characteristics of compound libraries needed to effectively span cell-division phenotype space, to find probes that target different mechanisms, are not known. Here we show that a small collection of 100 diaminopyrimidines (DAPs) yields a range of cell-division phenotypes, including changes in spindle geometry, chromosome positioning and mitotic index. Monopolar mitotic spindles are induced by four inhibitors, including one that targets Polo-like kinases (Plks), evolutionarily conserved serine/threonine kinases. Using chemical inhibitors and high-resolution live-cell microscopy, we found that Plk activity is needed for the assembly and maintenance of bipolar mitotic spindles. Plk inhibition destabilizes kinetochore microtubules while stabilizing other spindle microtubules, leading to monopolar spindles. Further testing of compounds based on 'privileged scaffolds', such as the DAP scaffold, could lead to new cell-division probes and antimitotic agents.