In laser processing, controlling the shape of the cutting profile, particularly the taper, is often essential. Understanding the interaction characteristics between the laser and the material, as well as the effects of processing parameters on the profile, is crucial. This study calculates the relationship between kerf angle and fundamental laser beam features during picosecond laser processing. Based on these results, two primary dicing modes—vibration mirror scanning and helical cutting—are examined. The influence of laser processing parameters on kerf angle in these modes is analyzed in conjunction with practical applications, enabling an understanding of the post-processing profile shape and estimation of relevant geometric parameters. Additionally, the paper discusses kerf angle control in other similar laser processing methods, analyzing their respective advantages and limitations to guide the selection of appropriate techniques for specific requirements.