Wear mechanisms including fracture and plastic deformation at the nanoscale are central to understand sliding contacts. Recently, the combination of tip-induced material erosion with the sensing capability of secondary imaging modes of AFM, has enabled a slice-and-view tomographic technique named AFM tomography or Scalpel SPM. However, the elusive laws governing nanoscale wear and the large quantity of atoms involved in the tip-sample contact, require a dedicated mesoscale description to understand and model the tip-induced material removal. Here, we study nanosized sliding contacts made of diamond in the regime whereby thousands of nm3 are removed. We explore the fundamentals of high-pressure tip-induced material removal for various materials. Changes in the load force are systematically combined with AFM and SEM to increase the understanding and the process controllability. The nonlinear variation of the removal rate with the load force is interpreted as a combination of two contact regimes each dominating in a particular force range. By using the gradual transition between the two regimes, (1) the experimental rate of material eroded on each tip passage is modeled, (2) a controllable removal rate below 5 nm/scan for all the materials is demonstrated, thus opening to future development of 3D tomographic AFM.