Globe artichoke (Cynara scolymus L.) is considered one of the most significant sources of phenolic antioxidants in nature. However, more than 60% of its total volume is discarded for consumption purposes, making available an abundant, inexpensive and profitable source of natural antioxidants in the discarded fractions. Polyphenolic antioxidants from a South American variety of artichoke agro-industrial discards (external bracts and stems) were obtained by mild extraction processes. Best results were achieved at 40 °C, 75% of ethanol and 10 min of reaction, obtaining 2.16 g gallic acid equivalent (GAE)/100 g of total phenolic compounds (TPC) and 55,472.34 µmol Trolox equivalent (TE)/100 g of antioxidant capacity (oxygen radical absorbance capacity (ORAC)). High-performance liquid chromatography (HPLC) analyses determined that caffeoylquinic acids comprise up to 85% of the total polyphenolic content, and only around 5% are flavonoids. Inulin content in the artichokes residues was recovered (48.4% dry weight (dw)), resulting in an extract with 28% of inulin in addition to the aforementioned antioxidant capacity. The artichoke discard extract in a concentration of 500 mg/L produced a strong decrease in Caco-2 and MCF-7 cancer cell lines viability, whereas healthy fibroblasts maintained their viability when the extract was concentrated at 1500 mg/L. These results suggest that the artichoke extract presents a good anti-proliferative potential effect on Caco-2 and MCF-7 cells.