The invention discloses a spark-erosion cutting machine capable of achieving slope cutting, and relates to the technical field of spark-erosion cutting machines. The spark-erosion cutting machine comprises a cutting machine body, wherein the top of the cutting machine body is connected with a supporting plate; the top of the supporting plate is connected with a top plate; the top of the top plate is connected with a water tank; and one side of the top of the top plate is provided with a water pump. According to the spark-erosion cutting machine capable of achieving slope cutting, through a clamp, an adjusting sleeve, a spring, a double-shaft motor, a connecting shaft and a supporting rod, the distance of the clamp is adjusted according to the size of a workpiece; the spark-erosion cutting machine adapts to various workpieces; when the length of a telescopic pipe needs to be increased, a threaded sleeve rotates clockwise and is in threaded connection with the telescopic pipe, the telescopic pipe makes lead screw move, and the telescopic pipe gradually extends towards the bottom of a cooling pipe under the action of the threaded sleeve; and when the angle of a spray head needs to be adjusted, due to the fact that the telescopic pipe is made of elastic materials, the angle of the spray head can be adjusted by directly rotating the telescopic pipe, and therefore the spray head is aligned with a machined part for cooling, and the cooling effect is improved.