Ten polyketide derivatives (1–10), including a new natural product named (E)-2,4-dihydroxy-3-methyl-6-(2-oxopent-3-en-1-yl) benzaldehyde (1), and five known diketopiperazines (11–15), were isolated from the mangrove-sediment-derived fungus Aspergillus sp. SCSIO41407. The structures of 1–15 were determined via NMR and MS spectroscopic analysis. In a variety of bioactivity screening, 3 showed weak cytotoxicity against the A549 cell line, and 2 exhibited weak antibacterial activity against methicillin-resistant Staphylococcus aureus (MRSA). Compounds 3, 5, and 6 showed inhibition against acetylcholinesterase (AChE) with IC50 values of 23.9, 39.9, and 18.6 μM. Compounds 11, 12, and 14 exhibited obvious inhibitory activities of lipopolysaccharide (LPS)-induced nuclear factor-κB (NF-κB) with IC50 values of 19.2, 20.9, and 8.7 μM, and they also suppressed RANKL-induced osteoclast differentiation in bone marrow macrophages cells (BMMCs), with the concentration of 5 μM. In silico molecular docking with AChE and NF-κB p65 protein were also performed to understand the inhibitory activities, and 1, 11–14 showed obvious protein/ligand-binding effects to the NF-κB p65 protein.