To improve the machining performance of different processing materials, a three-excitation ultrasonic spatial vibration-assisted turning system is proposed, which realizes the non-unity of the plane where the cutting trajectory of the tool is located. The influence and formation law of three-excitation ultrasonic spatial vibration-assisted turning on the surface roughness of the workpiece under different vibration parameters (amplitude) and machining parameters (cutting speed, cutting depth, and feed) were analyzed by response surface methodology. The results show that in terms of vibration parameters, the influence of ultrasonic vibration applied in the horizontal direction on surface roughness is significantly greater than that of ultrasonic vibration applied in the vertical direction, while the feed has the greatest influence on surface roughness, followed by cutting speed. The surface roughness of common turning, one-dimensional ultrasonic vibration-assisted turning, ultrasonic elliptical vibration-assisted turning, and three-excitation ultrasonic spatial vibration-assisted turning were theoretically analyzed and experimentally compared. The results show that compared with the other three turning methods, the three-excitation ultrasonic spatial vibration-assisted turning can obtain a lower surface roughness and have good machinability.