Saffron (Crocus sativus) floral by-products are a source of phenolic compounds that can be recovered and used in the nutraceutical, pharmaceutical, or cosmetic industries. This study aimed to evaluate the phenolic compounds’ extraction using green extraction techniques (GETs) in saffron floral by-products and to explore the influence of selected extraction techniques on the phytochemical composition of the extracts. Specifically, ultrasound-assisted extraction (UAE), subcritical water extraction (SWE), and deep eutectic solvents extraction (DESE) were used. Phenolic compounds were identified with (HR) LC-ESI-QTOF MS/MS analysis, and the quantitative analysis was performed with HPLC-PDA. Concerning the extraction techniques, UAE showed the highest amount for both anthocyanins and flavonoids with 50:50% v/v ethanol/water as solvent (93.43 ± 4.67 mg/g of dry plant, dp). Among SWE, extraction with 96% ethanol and t = 125 °C gave the best quantitative results. The 16 different solvent mixtures used for the DESE showed the highest amount of flavonoids (110.95 ± 5.55–73.25 ± 3.66 mg/g dp), while anthocyanins were better extracted with choline chloride:butane-1,4-diol (16.0 ± 0.80 mg/g dp). Consequently, GETs can be employed to extract the bioactive compounds from saffron floral by-products, implementing recycling and reduction of waste and fitting into the broader circular economy discussion.