Right knife radical (side-form of 刀) - anchors 刻 in the cutting family alongside 切 (cut), 划 (slash), 剪 (scissor), 削 (peel). The blade scores marks into wood, bronze or stone - also why 刻 came to mean 'a moment,' a tick carved on a water clock.
Left supplies the sound - hài drifted to kè through the regular k/h alternation. Same phonetic family: 该 (should), 孩 (child), 骇 (shocked), 咳 (cough). Pure phonetic loan; the boar meaning of 亥 contributes nothing semantic to 'carve.'
