Background: Curcuminoids, the bioactive compounds found in turmeric, exhibit potent antioxidant, anti-inflammatory, and neuroprotective properties. This study aims to enhance the extraction of curcuminoids from turmeric using environmentally friendly solvents supercritical CO2 (scCO2) combined with natural deep eutectic solvents (NADESs) in one process, and to evaluate the resulting biological activity. Methods: A Box–Behnken statistical design was applied to optimize scCO2 extraction conditions—pressure, CO2 volume, and temperature—to maximize curcuminoid yield. Next, the menthol and lactic acid NADESs were selected, and these two solvents were combined into a single turmeric extraction process. The biological activity of the resulting extract was evaluated using antioxidant assays (ferric reducing antioxidant power and 2,2-diphenyl-1-picrylhydrazyl) and enzyme inhibition assays (acetylcholinesterase, butyrylcholinesterase, and tyrosinase). Toxicity assessments were conducted on the aquatic invertebrates Daphnia pulex, Artemia sp., and Chironomus aprilinus. Results: The most effective extraction was achieved using a menthol–lactic acid NADES as a cosolvent, integrated at a 1:20 ratio of plant material to NADESs while in combination with scCO2. The optimized scCO2–NADES extraction resulted in a high curcuminoid yield (33.35 mg/g), outperforming scCO2 extraction (234.3 μg/g), NADESs ultrasound-assisted extraction (30.50 mg/g), and alcohol-based solvents (22.95–26.42 mg/g). In biological assays, the extract demonstrated significant antioxidant activity and effective inhibition of enzymes (acetylcholinesterase, butyrylcholinesterase, and tyrosinase). Toxicity studies showed a concentration-dependent response, with EC50 for Chironomus aprilinus at the level of 0.098 μL/mL and Daphnia pulex exhibiting high sensitivity to the extract. Conclusions: This study highlights the potential of combining NADESs and scCO2 extraction in one process, demonstrating the effectiveness of scCO2–NADES extraction in maximizing curcuminoid yield and enhancing bioactivity.