Developing cost-effective and high performance sodium-ion batteries (SIBs) relies mostly on advanced cathode materials with high electrode voltage, high capacity and fast sodium-ion diffusion. Here, we propose mixed sodium manganese oxides Nax(M0.44Mn0.56)O-2 (M = Mn, Fe, Co, Ni) as improved potential cathode materials for SIBs based on first-principles calculations. Our calculations reveal that these materials have relatively low volume expansion rates below 5%, and are thermodynamically stable. We find that the binding strength between the host and inserted Na atom gradually decreases as increasing the Na content x from 0.11 to 0.67 for each mixed compound, whereas it increases as going Mn -> Fe -> Co -> Ni at each value of Na content. Identifying the intermediate phases during Na insertion/extraction, we find a slight increase of electrode voltage with remarkably higher specific capacities by mixing due to extending the lower limit of Na content. We also investigate the sodium-ion diffusion by identifying plausible pathways , determining the activation barriers and diffusion coefficients , find fast migration within the S-shaped tunnel and moderate one within the small-sized tunnel. Through analysis of density of states, we find that these compounds exhibit half-metallic behaviour, demonstrating an enhancement of metallicity by mixing with higher valent transition metal atoms. Our calculation results show that these mixed compounds can be advanced cathode materials for high performance SIBs.