New brake-pad materials are inhomogeneous compounds with a variety of metallic and ceramic phases, whose interaction with the tool during the grinding operation is not fully understood. Yet, ground surface quality strongly influences the bedding-in phase. This research surveys how grinding operation affects the pad surface. The purpose is pursued by adopting an investigation protocol merging macroscopic outcomes with the study of chip-removal mechanisms and of the ground surface morphology in the microscale. A specific set of grinding tests is carried out on the friction material under different kinematic conditions. Macroscopic indicators of the process performances are measured and modeled. At a closer look, the ground surface shows a complex morphology that cannot be completely described by roughness values, but depends on how the various phases are distributed in the material and how they are affected by the tool during abrasion. A multiscale inspection procedure is proposed to assess the performances of a machining operation on complex materials, where the descriptive power of standard technological tests becomes inadequate.