Left mouth radical, pictograph of an open mouth, the indexing element. Marks 唾 as a mouth product: saliva and the act of spitting. Same family as 吐, 咽, 含, 嚼. The spit gesture also carries contempt in Chinese culture (唾弃 to scorn).
Right 垂 supplies the sound, drifting chuí to tuò through sibilant-shift. Vivid semantic flavour: 垂 means 'to hang down', and spittle is what hangs from a slack mouth or drops to the ground. The phonetic doubles as picture, a drop suspended and falling. Family: 锤, 捶, 睡.