The spindle is a dynamic intracellular structure self-organized from microtubules and microtubule-associated proteins. The spindle's bipolar morphology is essential for the faithful segregation of chromosomes during cell division, and it is robustly maintained by multifaceted mechanisms. However, abnormally shaped spindles, such as multipolar spindles, can stochastically arise in a cell population and cause chromosome segregation errors. The physical basis of how microtubules fail in bipolarization and occasionally favor nonbipolar assembly is poorly understood. Here, using live fluorescence imaging and quantitative shape analysis in Xenopus egg extracts, we find that spindles of varied shape morphologies emerge through nonrandom, bistable self-organization paths, one leading to a bipolar and the other leading to a multipolar phenotype. The bistability defines the spindle's unique morphological growth dynamics linked to each shape phenotype and can be promoted by a locally distorted microtubule flow that arises within premature structures. We also find that bipolar and multipolar spindles are stable at the steady-state in bulk but can infrequently switch between the two phenotypes. Our microneedle-based physical manipulation further demonstrates that a transient force perturbation applied near the assembled pole can trigger the phenotypic switching, revealing the mechanical plasticity of the spindle. Together with molecular perturbation of kinesin-5 and augmin, our data propose the physical and molecular bases underlying the emergence of spindle-shape variation, which influences chromosome segregation fidelity during cell division.