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Cancer and infectious diseases continue to be a major public health problem, and new drugs are necessary. As marine organisms are well known to provide a wide range of original compounds, the aim of this study was to investigate the bioactivity of the main constituents of the cosmopolitan red alga, Sphaerococcus coronopifolius. The structure of several bromoditerpenes was determined by extensive spectroscopic analysis and comparison with literature data. Five molecules were isolated and characterized which include a new brominated diterpene belonging to the rare dactylomelane family and named sphaerodactylomelol (1), along with four already known sphaerane bromoditerpenes (2–5). Antitumor activity was assessed by cytotoxicity and anti-proliferative assays on an in vitro model of human hepatocellular carcinoma (HepG-2 cells). Antimicrobial activity was evaluated against four pathogenic microorganisms: Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Candida albicans. Compound 4 exhibited the highest antimicrobial activity against S. aureus (IC50 6.35 μM) and compound 5 the highest anti-proliferative activity on HepG-2 cells (IC50 42.9 μM). The new diterpene, sphaerodactylomelol (1), induced inhibition of cell proliferation (IC50 280 μM) and cytotoxicity (IC50 720 μM) on HepG-2 cells and showed antimicrobial activity against S. aureus (IC50 96.3 μM).