Cells are the basic unit of biological organization, and their division is remarkably conserved across phyla. However from an evolutionary perspective, it remains unclear how much cellular parameters can diverge, without altering the basic function they sustain. We address the mechanics of asymmetric mitotic spindle positioning during the first embryonic division of six nematode species. We propose a viscoelastic model of spindle positioning and mobility that can provide a physical explanation of why in C. elegans it undergoes oscillations during elongation, whereas most others lack oscillations. To test this model, we measured the pulling forces and opposing cytoplasmic drag by a combination of laser ablation of the anaphase spindle and tracking of intracellular granules. While centrosomes of all species recoil on spindle cutting, quantitative differences correlate with the cytoplasmic viscosity. In fact, increased viscosity correlates with decreased oscillation speeds of intact spindles across species. However, the absence of oscillations despite low viscosity in some species, can only be explained by smaller pulling forces. Consequently, we find that spindle mobility across the species analyzed here is characterized by a tradeoff between cytoplasmic viscosity and pulling forces. Our work provides a framework for understanding mechanical constraints on evolutionary diversification of spindle mobility.