Particle mixing and segregation are ubiquitous in industrial processes, with their dynamic behavior being governed by both equipment geometry and particle attributes. Using the discrete element method (DEM), this study investigates the mixing characteristics of granular materials in a horizontal drum. Three quantitative metrics as the contact-based separation index, steady-state separation index, and average mixing rate are introduced to systematically evaluate the combined effects of drum width, particle density ratio, and particle size ratio on axial mixing performance under a constant drum diameter. The results demonstrate that the average mixing rate decreases with increasing drum width, but increases with higher density and size ratios. At a fixed drum width, mixing uniformity deteriorates as the density or size ratio increases. Both density and size differences induce radial and axial segregation, with radial segregation intensifying as these ratios increase. Notably, size difference also triggers axial segregation, the degree of which rises markedly with drum width. Kinetic analysis reveals that the higher radial kinetic energy compared to axial kinetic energy is the key reason for the superior radial mixing rate. Furthermore, the shear effect at the end-walls is identified as crucial for inducing axial particle flow. The differential impact of drum width on systems with density versus size differences stems from the distinct synergistic actions of buoyancy and percolation segregation mechanisms.