The application of an OSMAC (One Strain-Many Compounds) approach on the sponge-derived fungus Aspergillus sp. LS34, using two different media including solid rice medium and potato dextrose broth (PDB) resulted in the isolation and identification of two new compounds, named asperspin A (1) and asperther A (2) along with seven known compounds 3–9. Compounds 1–5 were detected in fungal extracts from rice medium, while compounds 6–9 were isolated from PDB medium. Their structures were unambiguously characterized by HRESIMS and NMR spectroscopic data. The growth inhibitory activity of these compounds against four pathogenic bacteria (Vibrio parahaemolyticus, Vibrio harveyi, Escherichia coli, and Staphylococcus aureus) were evaluated. All the compounds were also tested for their cytotoxicity against seven cancer cell lines, including CCRF-CEM, K562, BGC823, AGS, HCT-116, MDA-MB-453, and COR-L23. Among them, compound 9 showed strong activity against CCRF-CEM and K562 cells with IC50 values of 1.22 ± 0.05 µM and 10.58 ± 0.19 µM, respectively. Notably, compound 7 also showed pronounced activity against S. aureus with an MIC value of 3.54 µM.