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The application of biosorption operation has gained attention in the removal and retrieval of toxic metal ions from water bodies. Wastewater from industrial activity generally presents great complexity due to the coadsorption of cations to the inactive biomass binding sites. In this work, the competitive biosorption of Cu(II) and Ag(I) ions was studied in batch systems. A kinetic study applying a non-acidified and acidified waste of Sargassum filipendula in equimolar and non-equimolar metal samples was carried out and the acidified biosorbent was selected due to higher removal rates and selectivity of silver ions. The assays were performed with 2 g L−1 of biosorbent concentration at 25 °C for 12 h and pH was controlled at around 5.0. Copper presented higher affinity for the biosorbent and a fast biosorption kinetic profile, while silver equilibrium times exhibited dependence on the copper concentration. External diffusion is the rate-limiting step in Cu(II) ion removal and it might also limit the kinetic rates of Ag(I) ions with intraparticle diffusion, depending on the initial concentration of metal cations. The ion-exchange mechanism is evidenced and complexation and electrostatic attraction mechanisms might be suggested, explained by simultaneous chemisorption and physisorption processes during the operation. Calcium and sodium were released in considerable amounts by the ion-exchange mechanism. Characterization analyses confirmed the role of several functional groups in the competitive biosorption accompanied by a homogenous covering of both metal ions on the surface of the particles. Particle porosity analyses revealed that the material is macroporous and an appreciable amount of macropores are filled with metal cations after biosorption. [ABSTRACT FROM AUTHOR]