Carbon-based materials (e.g., C/C and C/C-SiC materials) are considered as promising brake disc materials for high-speed trains to replace cast or forged steels. Investigating the braking behavior of copper-based composites paired with various counterpart materials is helpful in advancing the development of high-speed and lightweight brake systems. In this study, the braking behavior and wear mechanisms of a novel copper-based composite mated with cast steel, C/C and C/C-SiC materials were investigated. The average coefficients of friction for the copper-based composite against C/C and C/C-SiC materials are increased by approximately 16.5% and 6.7%, and the wear rates of the copper-based composite against C/C and C/C-SiC materials are reduced by about 25.9% and 33.9% in comparison to those of the copper-based composite against cast steel. Additionally, compared with that of cast steel, the wear rate of the C/C material is increased by more than 3 times, and the negative value of the wear rate of the C/C-SiC material is noted. The dominant wear mechanisms of the copper-based composite mated with cast steel, C/C and C/C-SiC materials are adhesive wear combined with oxidation, graphite loss combined with oxidation as well as exfoliation of the material near graphite, and the material transfer combined with oxidation, respectively.