In recent years, new sources of secondary metabolites (SMs) in medicinal plants have been identified, and the introduction of these plants into field conditions has been carried out to obtain chemically diverse standardized raw material (RM). An example is mountain arnica Arnica montana L., one of Europe’s endemic endangered medicinal plant species, commonly used in pharmacy, cosmetics, and medicine. Its inflorescences (Arnicae flos) are characterized by anti-inflammatory, antiradical, antioxidant, antibacterial, antifungal, and antitumor properties. The main goals of the present research included: (i) characterization of the chemical composition of the inflorescences of A. montana harvested in different development stages; and (ii) presentation of the role of the development stage and different extraction methods in the antitumor activity of extracts through analyses of apoptosis, autophagy, and necrosis induction in human cervical carcinoma HeLa, human colon carcinoma HT29, and human colon metastatic carcinoma SW620 cell lines. The development stage was found to modify the composition of pharmacologically active substances, e.g., sesquiterpene lactones (SLs), flavonoids (Fs), and essential oil (EO), in arnica inflorescences. The content of Fs and EO increased during flowering to the full flowering phase; however, the highest content of SLs was noted in the full flowering phase and at the end of flowering. More promising results, i.e., a relatively high level of apoptosis and a low level of necrosis induced by the arnica extracts, were demonstrated in the HeLa cell line (full flowering; concentration: 0.5 µL/mL), the HT29 cell line (beginning of flowering; concentration: 0.5 µL/mL), and the SW620 cell line (stage of yellow buds; concentration: 1 µL/mL). This extremely valuable medicinal plant species provides a very broad range of RMs (e.g., inflorescences, rhizomes, roots, achenes, and all plant); therefore, attention should be paid to the more frequent use of water as a solvent in studies on the biological activity of mountain arnica extracts.