The remarkable mechanical properties of biological materials reside in their complex hierarchical architecture and in specific molecular mechanistic phenomena. The fundamental importance of molecular interactions and bond recovery has been suggested by studies on deformation and fracture of bone and nacre. Like these mineral-based materials, wood also represents a complex nanocomposite with excellent mechanical performance, despite the fact that it is mainly based on polymers. In wood, however, the mechanistic contribution of processes in the cell wall is not fully understood. Here we have combined tensile tests on individual wood cells and on wood foils with simultaneous synchrotron X-ray diffraction analysis in order to separate deformation mechanisms inside the cell wall from those mediated by cell-cell interactions. We show that tensile deformation beyond the yield point does not deteriorate the stiffness of either individual cells or foils. This indicates that there is a dominant recovery mechanism that re-forms the amorphous matrix between the cellulose microfibrils within the cell wall, maintaining its mechanical properties. This stick-slip mechanism, rather like Velcro operating at the nanometre level, provides a 'plastic response' similar to that effected by moving dislocations in metals. We suggest that the molecular recovery mechanism in the cell matrix is a universal phenomenon dominating the tensile deformation of different wood tissue types.