The second half of 咖啡, built the same way: mouth radical for 'borrowed drink sound', 非 for the phonetic. 咖 and 啡 are a bonded pair — neither means much alone, together they mean deadlines survived.
啡 rides wherever coffee goes: 拿铁咖啡 latte, 美式咖啡 Americano, 手冲咖啡 pour-over. Coffee vocabulary is one of the fastest-growing corners of modern Chinese — baristas in Chengdu debate 豆子 (beans) with sommelier vocabulary.
口 + 非: 'NOT 非 just any mouthful 口' — the second sip of COFFEE.
Decaf is 无因咖啡 'cause-less coffee' — caffeine 咖啡因 is literally 'the coffee cause', so removing it removes the 因.