Heat (HAE)- and ultrasound (UAE)-assisted extraction methods were implemented to recover anthocyanins from red raspberry. Processing time, ethanol concentration, and temperature or ultrasonic power were the independent variables combined in five-level rotatable central composite designs coupled with response surface methodology (RSM) for processes optimization. The extraction yield and levels of cyanidin-3-O-sophoroside (C3S) and cyanidin-3-O-glucoside (C3G) were monitored by gravimetric and HPLC-DAD-ESI/MSn methods, respectively, and used as response criteria. The constructed theoretical models were successfully fitted to the experimental data and used to determine the optimal extraction conditions. When maximizing all responses simultaneously, HAE originated slightly higher response values (61% extract weight and 8.7 mg anthocyanins/g extract) but needed 76 min processing at 38 °C, with 21% ethanol (v/v), while the UAE process required 16 min sonication at 466 W, using 38% ethanol (v/v). The predictive models were experimentally validated, and the purple-red extracts obtained under optimal condition showed antioxidant activity through lipid peroxidation and oxidative hemolysis inhibition, and antibacterial effects against food-related microorganisms, such as Escherichia coli and Enterococcus faecalis. These results highlight the potential of red raspberry extracts as natural food colorants with bioactive effects and could be exploited by industries interested in the production of anthocyanin-based products.