tie up
紮 centers on binding or fastening things together securely: tying up, bundling, or trussing.
紮 combines 札 (a wooden tag or slip) with 糸 (thread), suggesting the act of tying tags or bundles with string. The exact historical development is uncertain, but the component combination is consistent with the meaning of binding.
Picture a wooden tag 札 being tied to a bundle with thread 糸: the tag is secured by tying it up.
For サツ, imagine tying a bundle so tightly that it makes a sharp 'satsu' sound as the string pulls taut. The sound 'satsu' cues サツ while the bundle is tied up.