To obtain a functional part from additive manufacturing (AM) technologies, some surfaces require post-processing by machining. An approach is developed using additive manufacturing supports as a clamping device for the milling operation. A model combining an analytical approach to determine the cutting forces with a finite element model (FEM) to predict the dynamical response of the workpiece-supports system is proposed. The complex structure of the supports is homogenized with a simplified geometry with equivalent stiffness and mechanical properties. A case study from the biomedical field is proposed: the finishing operation of a custom-made maxillary reconstruction plate is simulated. A parametric study is proposed with: (1) two different lattice geometries used as support structures; (2) up and down milling; (3) different depths of cut.