Alginate is a naturally occurring polymer derived from brown algae biomass, which has numerous applications in various fields. Chemical modification of alginate is widely used to improve alginate’s physicochemical properties and provide new potential for multiple applications. In this article, we modified alginate with L-DOPA, using periodate oxidation and reductive amination, to obtain more suitable biopolymer for biocatalyst immobilization and hydrogel formation. Obtained modified alginate was used for the immobilization of laccase on cell walls. For this purpose, laccase from Streptomyces cyaneus was expressed on the surface of Saccharomyces cerevisiae EBY100 cells. The obtained cell wall laccase was immobilized within L-DOPA-alginate beads by crosslinking the L-DOPA-alginate with calcium ions and laccase. The effect of additional crosslinking of beads by green light-induced photopolymerization with eosin Y was investigated. The immobilized laccase systems were used for dye decolorization and investigated in multiple treatment processes. Beads with L-DOPA-alginate with a higher degree of modification (5.0 mol%) showed higher enzymatic activity and better decolorization efficiency than those with a lower degree of modification (2.5 mol%). Obtained immobilized biocatalysts are suitable for decolorizing dye Evans Blue due to their high efficiency and reusability.