Heart radical on the left marks 惭 as an inner state - shame is felt, not done. Same radical anchors the whole emotional vocabulary: 怕 fear, 悔 regret, 愧 ashamed (a near-synonym often paired with 惭 in 惭愧).
Right side supplies the sound: zhǎn drifted to cán (both initial and final shifted). 斩 contributes no semantic flavour here; it functions as a pure phonetic. The traditional form 慚 used the same phonetic with the full 心 radical underneath.
