Brown algae possess a diverse array of acidic polysaccharides, including fucoidan. The present research intends to investigate the extraction and characterization of algal polysaccharides to explore their antiviral activity. A light brown sulfated polysaccharide was extracted (with a yield of 18% of dry weight) from Sargassum asperifolium algal powder. The results of fractionation of sulfated polysaccharide revealed the occurrence of two primary fractions: low-sulfated polysaccharides (SPF1) and high-sulfated polysaccharides (SPF2). The bioassays conducted on SPF2 demonstrated a greater level of antioxidant activity compared to SPF1, with respective IC50 values of 17 ± 1.3 µg/mL and 31 ± 1.1 μg/mL after a duration of 120 min. The cytotoxicity of SPF2 on Vero cells was determined, and the calculated half-maximal cytotoxic concentration (CC50) was found to be 178 ± 1.05 µg/mL. Based on these results, an antiviral activity assay was conducted on SPF2. The results demonstrated that SPF2 had greater efficacy against Hepatitis A Virus (HAV) compared to Herpes Simplex Virus Type 1 (HSV-1), with corresponding half-maximal inhibitory concentrations (IC50) of 48 ± 1.8 µg/mL and 123 ± 2.6 µg/mL, respectively. The active SPF2 was characterized by FT-IR, 1H, and 13C NMR spectroscopy. The extracted fucoidan can be used as a natural therapeutic agent in combating various viral infections.