Plants belonging to the Rosa genus are known for their high content of bioactive molecules and broad spectrum of healing and cosmetic activities. Rosa platyacantha Schrenk is a wild-type species abundant in the mountainous regions of Kazakhstan. The phytochemical composition as well as the bioactivity of R. platyacantha extracts have not been fully investigated to date. In this study, various parts of R. platyacantha plant, collected in Almaty region, Kazakhstan, were used to prepare five hydroalcoholic extracts (R1–R5). The extracts were compared for the content of phytochemicals and selected biological activities, which are important for the potential cosmetic application of R. platyacantha. Extract R3, prepared from flower buds, showed the most significant antioxidant and tyrosinase inhibitory potential, decreasing the monophenolase and diphenolase activities of tyrosinase. Extract R3 showed also collagenase inhibitory activity and cytotoxicity against human melanoma cells A375, being less cytotoxic for noncancerous skin keratinocytes HaCaT. Analysis of fractions E and F, obtained from R3 extracts, revealed that quercetin, kaempferol, rutin, and their derivatives are more likely responsible for the tyrosinase inhibitory properties of R. platyacantha extracts.