sǎ is the physical-spread reading: grain, salt, petals, ashes, water — anything released so it spreads across an area. Distinct from sā (let go, let loose), which is figurative or colloquial. Object test: if what leaves the hand actually spreads out (seeds, sand), use sǎ; if it's a behavior or grip being released (a hand, a lie, anger), use sā.
culture
拿撒勒 (Nazareth) is one of the few transliterations to keep the sǎ reading. Most Catholic-era biblical names (撒旦, 撒罗满, 耶路撒冷) use sā. The split is historical convention rather than a rule; modern speakers often default to sā even for 拿撒勒.
Left indexing hand radical 扌 — the hand that does the scattering. Puts 撒 in the hand-action family with 抛 (toss), 扔 (throw). Picture fingers opening above a field, releasing grain in a wide arc — the hand is essential to the image.
Right 散 supplies the sound (sàn → sǎ with tone shift) and the meaning — 散 is 'to scatter / disperse.' The sǎ reading is the etymological core of 撒: hand (扌) + disperse (散) = hand-scattering.