A 23 W continuous wavelength $CO_2$ laser system exited by a high-frequency LCC resonant converter is adapted to cut a biodegradable rope fabricated with polybutylene succinate. As the biodegradable rope consists of three twisted strands, the thickness changes relative to the position of the laser beam and we thus propose a method to determine exact cutting depth. In order to obtain the parameters related to the rope cutting, the experimental and theoretical cutting depths are compared and analyzed for a range of laser heat sources. The melted thickness and groove width of the cut biodegradable rope are also examined. The proposed theoretical cutting depth depends on the incident power and target velocity ratio. From these experimental results, the biodegradable rope with a diameter of 22 mm can be cut with a heat source of 50 J/cm resulting in a melted thickness of 1.96 mm and a groove width of 0.65 mm. The laser system is shown to be perfect tool for the processing of biodegradable rope without the occurrence of raveling.