In a method for robot-controlled cutting of workpieces to be joined by laser radiation, a first workpiece is arranged in vicinity of a second workpiece in a first position. A laser is focused onto the first workpiece. A contour of the first workpiece is cut with the laser beam; this contour is to be assembled and joined with the second workpiece. During cutting, a first spacing of a focal point of the laser beam from the second workpiece is repeatedly determined in a distance direction that is identically oriented during cutting and is adjusted to a direction of assembling the first and second workpieces. During cutting, a second spacing of a processing point of the laser beam from the second workpiece is maintained at a constant value.