Stevia (Stevia rebaudiana) is processed industrially mainly for steviol glycosides, whereas its co-occurring chlorogenic acids—especially dicaffeoylquinic acids (diCQAs)—are emerging value-added food and feed ingredients. The stability of a commercial stevia chlorogenic acid product (total acids 61.39%; diCQAs 53.79%) was evaluated in the solid state and in 80% aqueous methanol under heat (80–180 °C), light, oxygen, metal-ion (Fe³⁺, Cu²⁺), pH (3.0–8.0), and solvent conditions. In solids, total acid loss remained below 10% at ≤140 °C (≤4 h) and was 2.12% at ≤100 °C for 24 h, but rose to 45.45% (160 °C) and 93.21% (180 °C) after 4 h; LC–MS revealed degradation, methylation, acetylation, and diCQA lactonization products that accumulated below 160 °C and degraded above 180 °C. In solution, total acid content was conserved at 60–80 °C, as acyl migration converted 4,5-diCQA and 5-CQA to more stable isomers. Fe³⁺ and Cu²⁺ formed reversible insoluble diCQA complexes (98.36–99.81% recovery after EDTA) that accelerated light- and oxidation-induced loss, Cu²⁺ more strongly. Hydrolytic loss predominated at pH 3.0–4.0 and was buffered by monomer interconversion at pH 5.0–8.0. These findings define a safe processing/storage window (≤140 °C solids; ≤80 °C, metal-ion-free, sealed opaque liquids) and provide a mechanistic basis for quality control.