While it has long been known that a large number of short-lived transient spirals can cause stellar migration, here we report that another mechanism is also effective at mixing disks of barred galaxies. The resonance overlap of the bar and spiral structure (SS) induces a nonlinear response leading to a strong redistribution of angular momentum in the disk. We find that, depending on the amplitudes of the perturbers, the changes in angular momentum, ΔL, could occur up to an order of magnitude faster than in the case of recurrent spirals. The signature of this mechanism is a bimodality in ΔL with maxima near the bar's corotation and its outer Lindblad resonance; this is independent of the properties of the SS. For parameters consistent with the Milky Way, the disk mixes in about 3 Gyr and the stellar velocity dispersion increases with time in a manner roughly consistent with observations. This new mechanism could account for both the observed age–velocity relation and the absence of age–metallicity relation in the solar neighborhood. Spiral–bar interaction could also explain observations showing that strongly barred galaxies have weaker metallicity gradients than weakly barred or non-barred galaxies.