Wear caused by hard debris or abrasive slurries trapped between moving surfaces is a major industrial problem concerning engineering and agriculture machine components, causing abrasion and reducing their service life. In this context, the wear of diamond tools used to cut stones represents an interesting case study due to the particular tribological interactions involved. Diamond tools are characterised by diamonds (the cutting edge) and the metal matrix (the retaining binder). While several attempts have been made to analyse diamond wear, the wear process involving the matrix is not yet well understood. In particular, the phenomena responsible for wear at the local scale have not yet been fully investigated as they are difficult to quantify experimentally and the existing numerical models, to the authors' knowledge, greatly simplify the physical behaviour and interactions between the different materials in contact. A new code is therefore used in this work. It is able to treat the metal matrix as a deformable polycrystalline material and the debris flow by controlling the shape and size of the grains. Furthermore, the wear of the metal matrix will be described as a loss of intergranular cohesion caused by the continuous passage of debris through a cohesive contact law that also takes fatigue into account. The model will show, albeit qualitatively, that the wear of the metal surface is caused by the asperities of the debris grains, thus validating one of the fundamental assumptions behind the model defined by the same authors at a larger scale. Another aspect investigated is the relationship between the temporal evolution of wear and the roughness of the metal surface. Again, it will be shown how the temporal evolution of the metal surface is consistent with what has been observed in the literature. Moreover, due to the complexity of the model, a sensitivity study will be necessary to understand the physical significance of the parameters and how to adapt them to the specific case study. It will then be shown how these parameters can change the physics of the problem being analysed and must therefore be chosen carefully.