amputate, cut off
劊 centers on severing or removing a part: amputating a limb or cutting something off cleanly.
劊 combines 會 (meeting, gathering) with 刂 (knife), suggesting a knife that cuts or severs. The exact historical development is uncertain, but the knife component clearly relates to cutting.
A meeting (會) with a knife (刂) ends with something being cut off. Imagine a gathering where a sharp blade amputates a limb.
For カイ, picture a knife cutting off a kite string: kite -> カイ, and the severed string falls away.