Adsorption is one of the most successful physicochemical approaches for removing heavy metal contaminants from polluted water. The use of residual biomass for the production of adsorbents has attracted a lot of attention due to its cheap price and environmentally friendly approach. The transformation of Sargassum—an invasive brown macroalga—into activated carbon (AC) via phosphoric acid thermochemical activation was explored in an effort to increase the value of Sargassum seaweed biomass. Several techniques (nitrogen adsorption, pHPZC, Boehm titration, FTIR and XPS) were used to characterize the physicochemical properties of the activated carbons. The SAC600 3/1 was predominantly microporous and mesoporous (39.6% and 60.4%, respectively) and revealed a high specific surface area (1695 m2·g−1). To serve as a comparison element, a commercial reference activated carbon with a large specific surface area (1900 m2·g−1) was also investigated. The influence of several parameters on the adsorption capacity of AC was studied: solution pH, solution temperature, contact time and Cr(VI) concentration. The best adsorption capacities were found at very acid (pH 2) solution pH and at lower temperatures. The adsorption kinetics of SAC600 3/1 fitted well a pseudo-second-order type 1 model and the adsorption isotherm was better described by a Jovanovic-Freundlich isotherm model. Molecular dynamics (MD) simulations confirmed the experimental results and determined that hydroxyl and carboxylate groups are the most influential functional groups in the adsorption process of chromium anions. MD simulations also showed that the addition of MgCl2 to the activated carbon surface before adsorption experiments, slightly increases the adsorption of HCrO4− and CrO42− anions. Finally, this theoretical study was experimentally validated obtaining an increase of 5.6% in chromium uptake.