Polysaccharides and protein–polysaccharide complexes produced from the fungal strain Trametes versicolor have demonstrated bioactive properties that depend on the substrate, the fermentation conditions and also the fungal strain. Likewise, the submerged and controlled fermentation of medicinal mushrooms elicits numerous advantages over traditional processes to produce mycelia and added-value products, along with the exploitation of biodiversity. This study evaluated the growth profile of an indigenous T. versicolor isolate using commercial nutrients that were subsequently replaced with renewable resources, specifically, grape pomace extract (GPE), under static and shaking conditions. The effect of elicitor addition was also assessed using GPE. The process productivity was significantly improved, yielding 21 g/L of biomass. Agitation proved beneficial for all examined cases regarding biomass productivity and substrate consumption rates. The chemical and antioxidant profile of crude intracellular and extracellular polysaccharides was determined, whereby intracellular extracts indicated >50% antioxidant activity. FTIR analysis validated the preliminary chemical characterization of the extracts, whereas the amino acid profile of IPS extracts was also included. Evidently, our study elaborates on the development of a bioconversion concept to valorize wine-making side-streams to formulate added-value products with potential bioactive attributes.