Left mouth radical — pictograph of an open mouth, the indexing element. Marks 叨 as a verbal action: chattering on and on (唠叨 to nag), or politely 'to receive' a favour (叨扰 sorry to trouble you, lit. 'to receive disturbance'). Family: 嘴, 唠, 嗨.
Right 刀 supplies the sound directly: dāo → dāo, no shift. Pure phonetic — no semantic contribution. The picture of a curved blade has nothing to do with chatter or politeness; chosen purely for the dāo sound. Same phonetic in 忉 (literary 'sorrowful'). One of the cleanest phono-semantic ratios.