咀 has two readings: jǔ ('to chew', the standard one — found in 咀嚼 jǔjué) and zuǐ (a popular variant of 嘴 'mouth', mostly seen in Cantonese place names like 尖沙咀 Tsim Sha Tsui). On the mainland, jǔ is the only reading you usually need.
口 depicts an open mouth — the obvious site of chewing. As radical it marks 咀 as a mouth-action verb, joining 吃喝嚼 — the eating-and-tasting family. Here it is fully literal: the jaw at work.
且 supplies the sound (qiě shifted to jǔ). The same phonetic also drives 沮阻姐助. Originally 且 depicted a stacked altar; in 咀 it carries phonetic load while the mouth radical handles the meaning.
