The utilization of materials with high strength to density ratio enables efficiency improvements and is therefore demanded for many applications, particularly in the aerospace and other mobility sectors. However, the machining of these typically difficult-to-cut materials poses a challenge for conventional manufacturing technologies due to the high tool wear. Abrasive water jet (AWJ) machining is a promising alternative manufacturing technology for machining difficult-to-cut materials, since the tool wear is low and material independent. However, AWJ machining is limited regarding the producible geometries when conducting cuts through a material. This limitation can be resolved with AWJ milling operations which on the other hand are time-consuming. To approach this challenge, an enhanced AWJ milling operation is presented and investigated in this paper with the aim to expand the producible geometries. This operation consists of two kerfs, inserted from different sides of the workpiece, which intersect at their kerf ground. Consequently, a piece of material is separated without the cut material being entirely chipped. Thus, the operation possesses a high aggregated material removal rate. The investigations presented in this paper show and evaluate the effects that occur during the milling of kerfs with variable depths on titanium aluminide TNM-B1. Furthermore, a method to compensate these effects is introduced and thus the producible geometries for effective AWJ milling could be enhanced.