Rare earth elements (REEs) are essential materials that play a key role in advancing modern technologies. The main sources of REEs are minerals such as monazite, bastnasite, and xenotime. Common extraction techniques include pyrometallurgy and hydrometallurgy, with the latter often preferred due to its higher efficiency, lower energy usage, and reduced air pollution. However, hydrometallurgy poses challenges, including the extensive use of strong acids, organic solvents, and the creation of considerable amounts of toxic secondary waste. This situation underscores the urgent need to develop more eco-friendly and less wasteful alternatives for extracting REEs. Supercritical fluid extraction (SCFE) emerges as a green technology for metal extraction, especially for REEs. In this study, we use a complex Canadian REE ore supplied by Avalon Advanced Materials as the primary material. We develop a unique method focusing on SCFE using supercritical carbon dioxide as the solvent, with a small amount of tributyl phosphate-nitric acid adduct serving as the chelating agent. To make this intricate ore suitable for SCFE and to achieve near-perfect REE extraction efficiency, a preliminary NaOH cracking step is applied. The optimization of various operational factors for both the NaOH cracking (including cracking temperature, NaOH to solid ratio, and caustic cracking duration) and SCFE (covering temperature, pressure, and the ratio of adduct to solid) is conducted using a comprehensive factorial design experiment method. A thorough examination of the ore samples was performed after the SCFE step to understand the mechanisms involved in the process.