Therapeutic treatments with Artemisia annua have a long-established tradition in various diseases due to its antibacterial, antioxidant, antiviral, anti-malaria and anti-cancer effects. However, in relation to the latter, virtually all reports focused on toxic effects of A. annua extracts were obtained mostly through conventional maceration methods. In the present study, an innovative extraction procedure from A. annua, based on pressurised cyclic solid–liquid (PCSL) extraction, resulted in the production of a new phytocomplex with enhanced anti-cancer properties. This extraction procedure generated a pressure gradient due to compressions and following decompressions, allowing to directly perform the extraction without any maceration. The toxic effects of A. annua PCSL extract were tested on different cells, including three cancer cell lines. The results of this study clearly indicate that the exposure of human, murine and canine cancer cells to serial dilutions of PCSL extract resulted in higher toxicity and stronger propensity to induce apoptosis than that detected by subjecting the same cells to Artemisia extracts obtained through canonical extraction by maceration. Collected data suggest that PCSL extract of A. annua could be a promising and economic new therapeutic tool to treat human and animal tumours.