cut off
斮 centers on severing or cutting something off, typically with a sharp tool. The meaning is straightforward and specific to the act of cutting off.
斮 combines 昔 (old times, past) with 斤 (axe). The axe component suggests cutting, while 昔 may contribute a phonetic element. The exact historical development is uncertain, but the character likely originally depicted cutting with an axe.
Imagine an old (昔) axe (斤) being used to cut off something from the past. The axe on the right does the cutting, while the left side reminds you it's an old, decisive action.
For サク, picture cutting off a sack (サク) with the axe: the sack is severed cleanly. Sack -> サク.