Growth variability generates mechanical conflicts in tissues. In plants, cortical microtubules usually align with maximal tensile stress direction, thereby mechanically reinforcing cell walls, and channeling growth rate and direction. How this is achieved remains largely unknown and likely involves microtubule regulators. The NIMA-related microtubule-associated kinase NEK6 phosphorylates tubulin, leading to the depolymerization of a subset of microtubules. We found that cortical microtubules exhibit a hyper-response to mechanical stress in the nek6 mutant. This response contributes to local cell protrusions in slow-growing regions of the nek6 mutant hypocotyl. When growth amplitude is higher, the hyper-alignment of microtubules leads to variable, stop-and-go, phenotypes, resulting in wavy hypocotyl shapes. After gravistimulation or touch, the nek6 mutant also exhibits a hyperbent hypocotyl phenotype, consistent with an enhanced perception of its own deformation. Strikingly, we find that NEK6 exhibits a novel form of polarity, being recruited at the ends of a subset of microtubules at cell edges. This pattern can be modified after local ablation, matching the new maximal tensile stress directions. We propose that NEK6 depolymerizes cortical microtubules that best align with maximal tensile stress to generate a noisier network of microtubules. This prevents an overreaction of microtubules to growth fluctuations and, instead, promotes the buffering of growth variations.