Synthetic samples of Ag(I) and Cu(II) cations were treated with acidified dealginated Sargassum filipendula, a modified waste from the thickener industry. Binary isotherms demonstrated a balance of simultaneous chemisorption and physisorption processes, pointing out to the presence of ion-exchange, chelation, and complexation mechanisms along with a preference for 2-plus-charged copper ions. Modified-extended Langmuir, noncompetitive Langmuir, and Langmuir-Freundlich models exhibited good fit to the experimental data, indicating the complex interactions among adsorbates, active sites, and other soft metals involved. The initial composition of the samples and the operation temperature demonstrated to influence the selectivity of the process. Maximum biosorption capacities were achieved at 30 °C for copper (3.60 mmol g−1) and silver (8.67 mmol g−1). Na2EDTA under acidic conditions was able to retrieve previously biosorbed copper ions selectively and at high rates even at very low concentrations of the chelating agent. HNO3 demonstrated high efficiency in removing silver from the biosorbent surface. It is suggested to recover selectively the metals, not only treating wastewater but also separating them for further purposes. XPS analysis marked the main role played by oxygenated groups in binding the adsorbates and the presence of Ag(I) and Cu(I) after the process could be detected. Copper reduction indicated chemical interactions and polarization effects due to the alginate net and elemental silver presence could not be discarded.