The article presents a review of research methods for the cutting process using the abrasive waterjet machining. The focus was on assessing the possibility of monitoring the cutting process based on the parameters available for direct or indirect measurement. An attempt was made to evaluate their influence on the machined surface after treatment with the abrasive cutting method. These parameters include, inter alia, vibrations of the cutting head, force effects on the head support structure and the material to be cut, dynamic properties of the machine support structure and high pressure pumps. As part of the own research, correlation was sought for the registered selected signal characteristics with the cutting parameters responsible for the process course and the parameters related to the obtained machined surface. For this purpose, a model of the deflection angle of the abrasive waterjet was proposed, which qualitatively determines the condition of the surface after cutting. The angle of inclination of the abrasive waterjet is determined on the basis of the registration of the feed force during the cutting process. The research on surface topography was extended by an attempt to determine the surface roughness by measuring vibrations and looking for correlation between the displacements of the cutter head tip and the measured roughness height profile. These tests also allowed the identification of selected frequencies that clearly result from the set parameters of the cutting process. The last stage of the research was to monitor the cutter head behaviour using a deformation sensor as another concept for recording the forces during the cutting process. Finally, the proposed methodology was characterized in the context of its usefulness in the on-line process monitoring and supervision system.