Laser-assisted ion-atom collisions are considered in terms of a nonperturbative quantum mechanical description of the electronic motion. It is shown for the system He(2+) - H at 2 keV/amu that the collision dynamics depend strongly on the initial phase of the laser field and the applied wavelength. Whereas electronic transitions are caused by the concurrent action of the field and the projectile ion at relatively low frequencies, they can be separated into modified collisional capture and field ionization events in the region above the one-photon ionization threshold.