A water-abrasive cutting system includes a cutting head (2) which includes a fixing device (16, 18, 20) for fixing the cutting head (2) on the wall to be cut as well as a nozzle head (10) disposed on the cutting head (2). At least one cutting nozzle (12), for an application of a cutting jet (14), is disposed in the cutting head (2). A cutting monitoring device (26) includes at least one hydrophone (30) and at least one further sensor. The cutting monitoring device (26) is configured to detect a complete penetration and/or cutting-through of the wall on the basis of the sensor signals of the hydrophone (30) and the at least one further sensor.