Interactions between microtubules and the cell cortex play a critical role in positioning organelles in a variety of biological contexts. Here we used Caenorhabditis elegans as a model system to study how cortex-microtubule interactions position the mitotic spindle in response to polarity cues. Imaging EBP-2::GFP and YFP::alpha-tubulin revealed that microtubules shrink soon after cortical contact, from which we propose that cortical adaptors mediate microtubule depolymerization energy into pulling forces. We also observe association of dynamic microtubules to form astral fibers that persist, despite the catastrophe events of individual microtubules. Computer simulations show that these effects, which are crucially determined by microtubule dynamics, can explain anaphase spindle oscillations and posterior displacement in 3D.