Background: Shirakiopsis indica (Willd.) (Family: Euphorbiaceae), a mangrove species found in the Asian region, is a popular folkloric plant. Locally, the plant is traditionally used to treat various types of ailments, especially for pain relief. Therefore, the current study investigates the neuropharmacological, antipyretic, thrombolytic, and anthelmintic properties of the S. indica fruit methanolic extract (SIF-ME). Methods: The neuropharmacological activity was evaluated using several bioactive assays, and the antipyretic effect was investigated using the yeast-induced pyrexia method, both in Swiss albino mice models. Human blood clot lysis was employed to assess thrombolytic activity, while in vitro anthelmintic characteristics were tested on Tubifex tubifex. Insights into phytochemicals from SIF-ME have also been reported from a literature review, which were further subjected to molecular docking, pass prediction, and ADME/T analysis and validated the wet-lab outcomes. Results: In the elevated plus maze test, SIF-ME at 400 mg/kg demonstrated significant anxiolytic effects (200.16 ± 1.76 s in the open arms, p < 0.001). SIF-ME-treated mice exhibited increased head dipping behavior and spent a longer time in the light box, confirming strong anxiolytic activity in the hole board and light–dark box tests, respectively. It (400 mg/kg) also significantly reduced depressive behavior during forced swimming and tail suspension tests (98.2 ± 3.83 s and 126.33 ± 1.20 s, respectively). The extract induced strong locomotor activity, causing mice’s mobility to gradually decrease over time in the open field and hole cross tests. The antipyretic effect of SIF-ME (400 mg/kg) was minimal using the yeast-induced pyrexia method, while it (100 μg/mL) killed T. tubifex in 69.33 ± 2.51 min, indicating a substantial anthelmintic action. SIF-ME significantly reduced blood clots by 67.74% (p < 0.001), compared to the control group’s 5.56%. The above findings have also been predicted by in silico molecular docking studies. According to the molecular docking studies, the extract’s constituents have binding affinities ranging from 0 to −10.2 kcal/mol for a variety of human target receptors, indicating possible pharmacological activity. Conclusions: These findings indicate that SIF-ME could serve as a promising natural source of compounds with neuropharmacological, anthelmintic, thrombolytic, and antipyretic properties.