Machining device for machining workpieces, the machining device comprising comprising - a tool spindle comprising -- a casing; -- a drive unit allowing a machining tool to be driven for rotation; and -- a clamping unit for clamping and releasing the machining tool, which clamping unit --- is arranged in the casing so as to be rotatable about an axis of rotation; and --- is drivable, by means of the drive unit, for rotation about the axis of rotation relative to the casing; -- a first supply channel for supplying a cooling fluid to the machining tool; and -- a second supply channel for supplying a fluid, in particular a lubricant-fluid mixture, to the machining tool, - a first provision unit for providing the cooling fluid; - a second provision unit for providing the fluid, in particular the lubricant-fluid mixture, and - a control unit for controlling the provision units (6, 8), characterized in that the control unit is configured in such a way that the following modes of operation are selectable: a) supplying the cooling fluid to the tool spindle without supplying the fluid, in particular the lubricant-fluid mixture, at the same time; b) supplying the fluid, in particular the lubricant-fluid mixture, to the tool spindle without supplying the cooling fluid at the same time; and c) supplying the cooling fluid and the fluid, in particular the lubricant-fluid mixture, at the same time. - a tool spindle comprising -- a casing; -- a drive unit allowing a machining tool to be driven for rotation; and -- a clamping unit for clamping and releasing the machining tool, which clamping unit --- is arranged in the casing so as to be rotatable about an axis of rotation; and --- is drivable, by means of the drive unit, for rotation about the axis of rotation relative to the casing; -- a first supply channel for supplying a cooling fluid to the machining tool; and -- a second supply channel for supplying a fluid, in particular a lubricant-fluid mixture, to the machining tool, -- a casing; -- a drive unit allowing a machining tool to be driven for rotation; and -- a clamping unit for clamping and releasing the machining tool, which clamping unit --- is arranged in the casing so as to be rotatable about an axis of rotation; and --- is drivable, by means of the drive unit, for rotation about the axis of rotation relative to the casing; --- is arranged in the casing so as to be rotatable about an axis of rotation; and --- is drivable, by means of the drive unit, for rotation about the axis of rotation relative to the casing; -- a first supply channel for supplying a cooling fluid to the machining tool; and -- a second supply channel for supplying a fluid, in particular a lubricant-fluid mixture, to the machining tool, - a first provision unit for providing the cooling fluid; - a second provision unit for providing the fluid, in particular the lubricant-fluid mixture, and - a control unit for controlling the provision units (6, 8), characterized in that the control unit is configured in such a way that the following modes of operation are selectable: a) supplying the cooling fluid to the tool spindle without supplying the fluid, in particular the lubricant-fluid mixture, at the same time; b) supplying the fluid, in particular the lubricant-fluid mixture, to the tool spindle without supplying the cooling fluid at the same time; and c) supplying the cooling fluid and the fluid, in particular the lubricant-fluid mixture, at the same time. a) supplying the cooling fluid to the tool spindle without supplying the fluid, in particular the lubricant-fluid mixture, at the same time; b) supplying the fluid, in particular the lubricant-fluid mixture, to the tool spindle without supplying the cooling fluid at the same time; and c) supplying the cooling fluid and the fluid, in particular the lubricant-fluid mixture, at the same time.