A laser cutting head includes a controllable collimator with movable collimator lenses for controlling beam diameter and/or focal point location. The laser cutting head may be used in a laser cutting system with a control system for controlling the position of the movable collimator lenses. The lenses may be moved, for example, to adjust the beam spot size for cutting different types of material or material thicknesses. The lenses may also be moved to adjust a focal point back to the workpiece after changing the distance of the laser cutting head relative to the workpiece.