The environmental concern with global Sustainable Development Goals (SDGs) has given researchers and industries more attention to using renewable resources and eco-friendly composite materials. However, conventional machining methods have drawbacks when machining natural composite materials. As a promising unconventional method, laser cutting has attracted the attention of manufacturing industries to machining composites, including natural fiber-reinforced polymer composites (NFRCs). Natural polymer composite materials, particularly those that use natural fibers as fillers, are trendy in a wide range of engineering applications. The challenge of this nontraditional method with NFRCs required the industries to demand extensive research into composite materials cutting properties and laser mechanisms. Using a long-pulse laser beam for cutting causes thermal effects during the material removal process. These effects include melting zones, heat-affected zones (HAZ), recast layers, and thermal damage to neighboring layers. This paper focuses on the overview of the laser machining concept in laser cutting processes and their advantages in cutting NFRCs. The final product applications of the NFRCs determine the laser machining strategies. The laser cutting performance analysis associated with machining challenges and essential process parameters that affect the cutting kerf quality and the HAZ is outlined for a better fundamental understanding in this research area. Future research into laser cutting mechanisms on NFRCs could benefit from new combinations of laser type, process parameters, and selected composition of NFRCs.