The artichoke (Cynara cardunculus L. subsp. scolymus) is an endemic perennial plant of the Mediterranean area commonly consumed as food. It is known since ancient times for its beneficial properties for human health, among which its antioxidant activity due to polyphenolics stands out. In the frame of our ongoing studies aiming to highlight the biodiversity and the chemodiversity of natural resources, we investigated the phenolic and saponin content of the cultivar “Carciofo di Procida” collected at Procida, an island of the Gulf of Naples (Italy). Along with the edible part of the immature flower, we included in our analyses the stem and the external bracts, generally discarded for food consuming or industrial preparations. The LCMS quali-quantitative profiling of polyphenols (including anthocyanins) and cynarasaponins of this cultivar is reported for the first time. In addition to antioxidant properties, we observed a significant cytotoxic activity due to extracts from external bracts against human neuroblastoma SH-SY5Y cell lines with 43% of cell viability, after 24 h from the treatment (50 μg/mL), and less potent but appreciable effects also against human colorectal adenocarcinoma CaCo-2 cells. This suggests that the different metabolite composition may be responsible for the bioactivity of extracts obtained from specific parts of artichoke and foresees a possible exploitation of the discarded material as a source of beneficial compounds.