The biorefinery concept facilitates the extraction of different constituents from seaweed, ensuring full usage of resources and generating few residues through a succession of steps. Innovative and environmentally-friendly extraction techniques, dubbed “green processing technologies,” have been developed in recent years. Using the bioprocess simulation software SuperPro Designer®, a model was developed and used to demonstrate the feasibility of two different multi-product biorefinery scenarios applying green technologies to one of the most promising species in Europe, the brown alga Saccharina latissima (sugar kelp). Analyzing the current state of the art and commercial applications, enzyme-assisted extraction was chosen as an emerging sustainable technology to simulate the production of alginate and the functional saccharides laminarin and fucoidan. These simulations were compared to an additional simulation of alginate production using the low-yield alkaline extraction technique currently used in the industry, which has been proven not feasible for the expected prices of cultivated seaweed in Europe. Complete biomass valorization is achieved by the sub-processing of the by-streams into complementary products such as biostimulants and animal feed. The valorization of up to 1.07 € per kilogram of fresh weight biomass was achieved using enzyme-assisted extraction and prioritizing laminarin and fucoidan as main products. Extraction yields and raw biomass alginate composition have the largest sensitivity effects on the profitability of biorefineries. This provides further insight into the crucial research opportunities on downstream processing and seaweed cultivation targets.