Wood cutting can be described as an interaction between a tool and a material causing complex local deformations. This material response to loading takes place at a scale where the size of the involved process is in the range of the cell wall dimension, which makes it difficult to be described analytically, therefore, often semi-empirical or statistical models are used for modeling the process and derive cutting forces and power for the design of machines, tools and processes. Nevertheless, analytical models have the advantage of granting deeper insight into processes and interactions, where statistical or machine learning models might fail. One of these models, originally developed for metal cutting, combines fracture mechanics with strengths of materials and provided insight into the general functionality between uncut chip thickness and force per width and it is based on the material parameters strength and fracture energy combined with cutting geometry. Several publications show the suitability of this approach to the wood cutting process. Nonetheless, both material parameters require additional, specialized experiments and effort. Statistical models alternatively show strong correlation of cutting forces with density. Motivation for this work was to combine these ideas and predict strength and fracture energy by their related density using a foam model, and therefore, reduce the cutting equation to minimum set of parameters and generalize it at the same time for the prediction of cutting forces in a range of densities. Besides the theoretical work, experiments on several wood species in orthogonal cutting conditions parallel to wood grain and perpendicular were performed and showed sufficient agreement with the new scaling law.