A controller of a cutting apparatus obtains cutting data and specifies a pressure value corresponding to pressure to be applied to an attaching portion by a pressure changer during cutting processing for cutting a workpiece using a cutting blade based on the cutting data and a target range defining target positions of the attaching portion in a fifth direction. While causing the pressure changer to apply, to the attaching portion, the pressure corresponding to the specified pressure value, the controller executes the cutting processing by controlling a first moving mechanism and obtains the position of the attaching portion in the fifth direction. If the obtained position of the attaching portion is out of the target range, the controller changes the pressure value to another value and executes the cutting processing while causing the pressure changer to apply, to the attaching portion, the pressure corresponding to the other value.