Left two-stroke ice radical — replaces traditional 氵 (water) in the simplified 减. The shift from water to ice carries a faint semantic resonance: water reduced and frozen down. Same ice radical in 冷 (cold), 冻 (freeze), 凉 (cool). Traditional 減 used the full water radical instead.
Right 咸 supplies the sound (xián → jiǎn, related Old Chinese onset). 咸 itself shows 戌 (halberd) over 口 (mouth), historically meaning 'all, complete.' Same phonetic family: 喊 (shout), 感 (feel), 憾 (regret) — all carry the xián / gǎn / hǎn cluster.
