Stone radical on the left — pictures a rock at the foot of a cliff (厂 + 口). It supplies the meaning here: 破 originally described stone being smashed or split. From that concrete sense came every kind of breaking: 打破 (break), 突破 (break through), 破坏 (destroy).
皮 (pí) supplies the sound, with a tone shift to pò. It pictures a hand peeling a hide, which gives 破 a faint flavor of stripping/tearing in addition to the smashing-stone sense from 石. Same phonetic anchors 波 (wave), 坡 (slope), 披 (drape over).