establish, create, knife cut
刱 centers on the act of bringing something into being: establishing or creating. The 'knife cut' sense is a specific physical application of that creative or initiating action.
The exact historical development of 刱 is uncertain. It visually combines 井 (well) and 刂 (knife), but the original semantic or phonetic motivation is not clearly established.
Picture a well 井 being cut open with a knife 刂 to establish a new water source. The act of cutting creates something new.
For ソウ, imagine the sound of a saw cutting through wood to create something: saw -> ソウ, and the knife 刂 establishes a new shape.