A method for cutting machining of turbine blades (1) on a multi-axis machine tool, the turbine blade (1) is held by a rotatable blade-root clamping device and a rotatable blade-tip clamping device (2) and is machined by means of a tool which is chucked in a tool spindle. A first profile section (4) which is adjacent to the blade tip is first of all machined by the tool and the tool is then removed. The tool spindle then grabs an already horizontal additional clamping device (5) which has clamping jaws (6.1, 6.2) adapted to the first profile section (4). The additional clamping device (5) is positioned on the blade-tip clamping device (2) in such a way that the clamping jaws (6.1, 6.2) rest in the first profile section (4). The tool spindle then grabs a tool and machines the remaining profile section with it.