Addition of alloying elements to pure metals is a well known and efficient method to tune the final properties of the material. Nevertheless, further cold working can shift desired properties. As an example of the extreme state of introduced excessive strain to the material sever plastic deformation (SPD) techniques can be noted. Interactions between alloying elements and crystalline defects may lead to the formation of metastable phases or unusual nanoscaled structures. Initial phase and the chemical composition may also significantly affect final structure and, thus, properties. For efficient materials design and further expanding of severe plastic deformation processing techniques as a flexible way of direct changes of microstructure and, thus, properties of new materials, this aspect should be studied. To shed some light on the effects related to the interaction between nanoscaled structure and alloying elements and its influence on final properties of obtained materials, a binary Cu -- Be alloy with known precipitation kinetics  was subjected to high-pressure torsion at different phase and chemical compositions. Using a complex of experimental techniques (TEM/STEM, XRD, DCS, mechanical properties measurements) it was found that initial precipitation and amount of alloying element can affect final grain size, thermal stability, mechanical properties and even strain accommodation mechanisms during processing. Results of this work show that these aspects are worth to be taken in to account while developing a new alloys for further SPD-processing.