Laser-based cutting can deliver high accuracy and speed during the process. However, there are still some technical challenges to be solved. First, the process itself requires precise focusing of the laser beam. When using continuous wave (CW)- or pulses in the μs- to ns-range for efficient materials removal, not only the targeted material volume is heated, but also the surrounding material due to heat diffusion. This decreases the quality of the cut. Coupling the light into a water-jet solves both issues: It ensures the delivery of focused light to the target surface, while cooling the affected material during processing. This work proposes a real-time monitoring system of the cutting process by exploiting unique physical phenomena related to the process. The water jet allows both the propagation of laser light towards the target while keeping it focused and the back-propagation of process light through the focusing system. This can be captured using suitable sensors, and saved using a data acquisition system. The acquired data can be used for process characterization using signal processing. In this work we demonstrate the direct correlation between different process parameters and statistical signal features. We show that reducing the signal to a few statistical features both in time and frequency by feature extraction does not reduce the information content, but instead makes it more robust to mis-classification while decreasing the classification time. It also opens up a wide range of future applications not only to process data, but also to control the process more precise.