Right
叕 supplies the sound - zhuó drifting to chuò through the regular z/ch palatalisation.
叕 is the rare graph depicting four
又 (right hands) interconnected, the original form behind
缀 (sew together) and
辍 (interrupt). Same phonetic series gathers join-and-stop meanings. For
啜 the connecting picture suits: the lips repeatedly closing on the rim of a cup as one sips.