FeTi–Cu composites with varying Cu contents are subjected to high-pressure torsion, and their deformation behavior is explored systematically using scanning electron microscopy, microhardness, and nanoindentation. The study identifies the limiting factors influencing the refinement during severe plastic deformation. The pronounced strength differences between phases lead to fragmentation primarily through hard–hard (FeTi–FeTi) contact points, promoted by homogeneous, i.e., nonlocalized, and possibly turbulent material flow. These conditions are prevalent in Cu-rich composites and during high-temperature deformation. Conversely, Cu-lean composites exhibit deformation localization, hindering the fragmentation process. Abrasion becomes an efficient refinement mechanism at the submicron-/nanoscale, particularly for composites containing higher concentrations of nanocrystalline FeTi and exhibiting homogeneous plastic deformation. Consequently, deformation localization in Cu-lean composites inhibits both refinement mechanisms, while Cu-rich compositions and higher temperatures result in efficient refinement but at the risk of coarsening at the nanoscale. Refinement is localization-limited in the former case and abrasion-limited in the latter. Optimized processing conditions can overcome these constraints, yielding a uniform nanocomposite. This study sheds light on the intricate interplay of the mechanical properties of the respective phases in a composite, emphasizing the importance of tailored compositions and deformation conditions to optimize nanocomposites, particularly when dealing with challenging material pairings.