The paper deals with the automation of the hydroabrasive production process, which leads to higher productivity and production optimization. In the submitted work, the basis of control design is a topography function of surface roughness of abrasive waterjet cut walls, and its functional relations to the controlled speed and to the measured mean values of sound pressure level, including a design of a suitable diagram of connections of controlling elements and equipment. The controlled parameter is the final roughness of a cut wall; in the design, the roughness is program-regulated according to the continuously measured root mean square of sound pressure level by means of continuous control of the traverse speed of cutting head.