horse whip, flog
箠 centers on a tool for striking or driving: a horse whip, or the act of flogging. Both meanings share the idea of using a long, flexible implement to deliver a sharp blow.
箠 combines 竹 (bamboo) with 垂, which likely contributes the sound and may relate to hanging or drooping, perhaps suggesting a flexible bamboo whip.
Bamboo 竹 hangs down 垂 like a flexible whip: 箠 is a horse whip made of bamboo, used for flogging.
For スイ, imagine a whip swinging through the air with a sharp 'swish' sound: swish -> スイ, and the bamboo whip cracks down.