In the field of manufacturing engineering, process designers conduct numerical simulation experiments to observe the impact of varying input parameters on certain outputs of the production process. The disadvantage of these simulations is that they are very time consuming and their results do not help to fully understand the underlying process. For instance, a common problem in planning processes is the choice of an appropriate machine parameter set that results in desirable process outputs. One way to overcome this problem is to use data mining techniques that extract previously unknown but valuable knowledge from simulation results. This paper presents a hybrid machine learning approach for applying clustering and classification techniques in a laser cutting planning process. In a first step, a clustering algorithm is used to divide large parts of the simulation data into groups of similar performance values and select those groups that are of major interest (e.g. high cut quality results). Next, classification trees are used to identify regions in the multidimensional parameter space that are related to the found groups. The evaluation shows that the models accurately identify multidimensional relationships between the input parameters and the output values of the process. In addition to that, a combination of appropriate visualization techniques for clustering with interpretable classification trees allows designers to gain valuable insights into the laser cutting process with the aim of optimizing it through visual exploration.