Chalcone is an aromatic ketone that forms the central core of many important biological compounds. Chalcone derivatives show various biological activities, especially anti-inflammatory, antibacterial, antioxidant, and anticancer activities, and also inhibit melanoma cell growth. In this study, we synthesized chalcone compounds with bis-chalcone’s chemical structure under microwave (MW) and microwave–ultrasound (MW-US) conditions and compared them to chalcones produced using the classical synthesis method. All bis-chalcones were synthesized with terephthalaldehyde and an appropriate aromatic ketone as substrates in Claisen–Schmidt condensation. All the obtained compounds were tested regarding their roles as potential anticancer agents. The cytotoxic effect of the bis-chalcones against human MeWo and A375 melanoma cell lines was investigated through colorimetric MTT and SRB assays. The data were analyzed statistically. In the case of the synthesis of bis-chalcones, it was determined that the use of green conditions supported by the MW or MW-US factors led to an increase in the yield of the final products and a reduction in the reaction time compared to the classic method. The biological results showed the high cytotoxic effect of bis-chalcones. The present results show the compounds’ high antiproliferative and cytotoxic potential, especially for the two selected bis-chalcone derivatives (3b and 3c), in particular, at concentrations of 50 μM–200 μM at 24, 48 h, and 72 h of incubation. The use of MW and US for the synthesis of bis-chalcones significantly improved the process compared to the classical method. The derivatives containing two hydroxy and two methoxy groups were the most effective against the tested cancer cells.