This study focused on stress and strain analysis of the cutting force of a branch knife with a replaceable cutting edge. The replaceable edge forms part of the delimbing head, which is applied to the arms of a mechanical harvester working in forestry. Basic parameters of the knife and head of the harvester with the basic calculations necessary to determine the number of knives based on input parameters, such as wood diameter, woody plants, and determination of the cutting force acting on the cutting knife, were examined. Based on the cutting force and the design of the special cutting knife, a stress analysis and a finite element method (FEM) was performed. This study confirmed the correctness of the selected material to produce the delimbing knife, which was designed using a replaceable cutting edge. The output of the stress analysis is reported.