Machining processes of composites are common operations in industry involving elevated risk of damage generation in the workpiece. Long fiber reinforced polymer composites used in high-responsibility applications require safety machining operations guaranteeing workpiece integrity. Modeling techniques would help in the improvement of machining processes definition; however, they are still poorly developed for composites. The aim of this paper is advancing in the prediction of damage mechanisms involved during cutting, including out-of-plane failure causing delamination. Only few works have focused on three-dimensional simulation of cutting; however, this approach is required for accurate reproduction of the complex geometries of tool and workpiece during cutting processes. On the other hand, cohesive interactions have proved its ability to simulate out-of-plane failure of composites under dynamic loads, as impact events. However, this interlaminar interaction has not been used up to date to model out-of-plane failure induced during chip removal. In this paper, both a classical damage model and cohesive interactions are implemented in a three-dimensional model based on finite elements, in order to analyze intralaminar and interlaminar damage generation in the simplified case of orthogonal cutting of carbon LFRP composite. More realistic damage predictions using cohesive interactions were observed. The strong influence of the stacking sequence on interlaminar damage has been demonstrated.