The only commercially relevant source for natural rubber (NR) is the Para rubber tree, Hevea brasiliensis. The need to find new sources of NR is increasing rapidly due to challenges from climate change and environmental impacts. NR from Taraxacum kok-saghyz (TKS) is a promising alternative. To compete with the pricing of NR from the rubber tree, an economically viable extraction system with a high output of NR is needed. The mechanisms involved in the separation of rubber from other plant constituents and potential rubber agglomeration during mechanical extraction processes are described through experimental results but not as extraction models. To analyze these mechanisms, two different wet-mill extraction system setups are investigated in this study: single-stage extraction and two-stage extraction with premilling. Two extraction models for mechanical rubber extraction mechanisms are identified and described: (i) the Model of Rolling Shear Mechanism with mild extraction behavior and rubber agglomeration, and (ii) the Model of Abrasion Shear Mechanism, which limits the rubber yield and promotes fast rubber agglomeration. The insights into the mechanisms are described and discussed through sieve analysis, rubber yield, dirt content, microscopic analyses, and viscoelastic analyses of the extracted rubber.