Environmental and hormonal signals cause reorganization of microtubule arrays in higher plants, but the mechanisms driving these transitions have remained elusive. The organization of these arrays is required to direct morphogenesis. We discovered that microtubule severing by the protein katanin plays a crucial and unexpected role in the reorientation of cortical arrays, as triggered by blue light. Imaging and genetic experiments revealed that phototropin photoreceptors stimulate katanin-mediated severing specifically at microtubule intersections, leading to the generation of new microtubules at these locations. We show how this activity serves as the basis for a mechanism that amplifies microtubules orthogonal to the initial array, thereby driving array reorientation. Our observations show how severing is used constructively to build a new microtubule array.