The supports in additive manufacturing can be used in an innovative way by being considered as supports for machining operation. This innovative use of manufacturing supports can facilitate the finishing of functional thin structures. But the flexible global workpiece-supports system can potentially cause vibrations during the machining operation. This can cause irregular surfaces with bad quality. This study highlights the importance of additively manufactured support structures on the stability of Ti-6Al-4V parts milling by using supports as a machining fixture. Nowadays, the control of the support stiffness and mechanical properties is not proposed by specific AM software. A way to develop a numerical method to optimize the post-processing of additive manufacturing parts is to use specific lattice structures as supports. Indeed, by adjusting the topology and the beam diameter of lattices, the relative stiffness and the relative density of the global structure can be controlled. The objective of this study is to show that the stiffness of the manufacturing supports is crucial for the machining operation. To validate this concept, milling tests are proceeded on thin-walled plates produced by Selective Laser Melting (SLM) using defined finish milling cutting conditions. Three types of results are obtained: cutting forces signals, displacements and surface qualities by confocal microscopy. The study reveals that milling can induces chatters. Also, surface qualities and dimensional deviations depend on the support choice. The control of mechanical properties of support structures appears to be a good way to favor machining operation of flexible and thin-walled structures. Topology and dimensional parameters of supports have to be considered in preliminary design steps of the additive manufacturing digital chain.