The ability to perform fast, accurate, deformable registration with intraoperative images featuring surgical excisions was investigated for use in cone-beam CT (CBCT) guided head and neck surgery. Existing deformable registration methods generally fail to account for tissue excised between image acquisitions and typically simply "move" voxels within the images with no ability to account for tissue that is removed (or introduced) between scans. We have thus developed an approach in which an extra dimension is added during the registration process to act as a sink for voxels removed during the course of the procedure. A series of cadaveric images acquired using a prototype CBCT-capable C-arm were used to model tissue deformation and excision occurring during a surgical procedure, and the ability of deformable registration to correctly account for anatomical changes under these conditions was investigated. Using a previously developed version of the Demons deformable registration algorithm, we identify the difficulties that traditional registration algorithms encounter when faced with excised tissue and present a modified version of the algorithm better suited for use in intraoperative image-guided procedures. Studies were performed for different deformation and tissue excision tasks, and registration performance was quantified in terms of the ability to accurately account for tissue excision while avoiding spurious deformations arising around the excision.