For most wood-based product uses it is essential to remove a large part of the water content from wet or green (fresh-cut) wood, to reduce further dimensional variations under varying humidity conditions, improve its mechanical characteristics, and protect it from biological attacks. However, the internal mechanisms of drying are not fully described. Here we observe drying at different scales using macroscopic measurements (weighing), nuclear magnetic resonance measurements allowing to distinguish bound- and free-water contents, and x-ray computed tomography images of air-liquid interfaces at the smallest pore scale (wood lumens). We show that during wood drying, even well above the fiber saturation point, bound water diffusion in cell walls (instead of capillary effects) ensures the extraction of liquid water from pores and its transport towards the surface of evaporation, and thus controls the drying rate. The distribution of bound-water content (uniform or heterogeneous) along the main sample axis and the drying-rate evolution depend on the competition between the external conditions and a characteristic rate of transport due to bound-water diffusion. For sufficiently slow drying this distribution remains homogenous until free water is fully extracted. An original physical phenomenon is thus at work, which plays a major role in regulating water extraction, in that it maintains a constant drying rate and a homogeneous distribution of the (mean) water content throughout the material. These results provide sound concepts for modeling and controlling drying properties of wood materials. They open the way to the understanding or control of the properties of many other materials containing two water types in food or civil-engineering applications. Our results complete recent observations that bound-water diffusion also controls imbibition in hardwood and finally show that transfers between bound and free water play a major role in the interaction of plantlike systems with water.