Think of a line drawn on the floor of an airport. Goods that cross that line into a country normally have a tax added to them, and the price goes up. Duty-free is the small opening in that rule: the tax has simply been left off, so the same bottle costs less on this side of the line than it will on the other. Everything the word does grows out of that missing tax — the goods it is missing from, the bag you carry them home in, and the shop that is allowed to sell them that way.
Wiktionary analyses the word as duty plus the suffix -free. Duty is the tax charged on goods entering a country, and -free means without, as in tax-free or sugar-free. So the word says, in its own parts, that the tax has been left off.
Wiktionary 把這個字拆成 duty 加上字尾 -free。duty 在這裡指貨物進入一個國家時要繳的稅。-free 是「沒有、免掉」，跟 tax-free、sugar-free 的 -free 一樣。所以這個字的組成本身就說出了核心畫面：那筆稅沒有被加上去。
Wiktionary entry for duty-free (packet source_ref kaikki:3f6f69a190036ae4:1328602987:11915): From duty + -free.
Two branches
少掉那筆稅的東西
最貼近核心畫面的一組：先說東西有這個性質，再直接用同一個字指那些東西。
adjective · B1
Duty-free goods are goods that you can buy and bring into a country without paying the tax that is normally charged on them; the word is also used of the shops, prices and allowances where this is true.
免稅的
賣這些東西的那個地方
從商品跳到賣商品的店；英文常這樣用商品的名字稱呼店面。
noun · B2
A shop, usually inside an airport or on a ship, that sells goods without the usual tax on them.
免稅店