This paper presents results from laboratory direct shear tests and discrete element method (DEM) simulations of railway ballast mixed with different contents of tire derived aggregate (TDA). The stress-strain behavior of the ballast-TDA mix was obtained. The results from laboratory tests and DEM simulations were compared. The laboratory and DEM tests both showed that the TDA significantly decreased the peak shear stress and the dilation effect of the ballast-TDA mix. According to the Mohr-Coulomb failure criterion, the TDA decreased the cohesion strength and the internal friction angle of the ballast-TDA mix. The DEM simulations provided insights into the microscopic behavior of ballast-TDA mixture through the coordination number (CN) and contact force distribution. The DEM simulation showed that the TDA increased the CN among the particles. As the content of TDA increased, the CN of TDA increased while the CN of ballast particles decreased. The TDA tended to decrease the occurrence of large contact forces ($>$250 N), and thus lowered ballast breakage in the ballast-TDA mix.