Picture a pair of scissors coming down on something that was joined up a moment ago. What the word keeps is not the movement but what the movement leaves behind: the point where the join ends, and the raw edge next to it. Cut the pipe and the water stops arriving. Cut the calendar and nothing after that day is counted. Cut the trouser leg and what is left is a pair of shorts.
Wiktionary records cut-off as a deverbal noun from the verb 'cut off'. The noun takes the action and freezes it into the place where the cutting happened, which is why one word can name a date, a stoppage and a piece of clothing.
來源資料記 cut-off 是從動詞片語 cut off 名詞化而來（deverbal）。名詞把那個動作凍住，留下的是「剪在哪裡」這個位置。所以同一個字才能同時指一個日期、一次中斷，和一件褲子——它們都是同一刀留下的痕跡。
Wiktionary entry 'cut-off' (kaikki source_ref 3f6f69a190036ae4:1479680306), etymology_text: 'Deverbal from cut off.'
From the picture
在時間或數字上畫一刀
同樣是那一刀，只是這次剪的不是水管，而是一條看不見的線：日期、分數、年齡、金額。被剪開的兩邊，一邊算數，一邊不算。所以 cut-off date 給人的感覺是硬的——差一天就在線外，不是誰在生氣，是規則到那裡就停了。
noun · B1
The point at which something stops or is no longer accepted — a date, time, number or score that has been fixed as the limit.
截止點；門檻
布料上真的那一刀
這一家不是比喻，是字面：剪刀真的落在布上。也因為這樣，它最能幫學習者記住整個字——先看得懂剪短的牛仔褲，再去理解被剪斷的水和被剪斷的日期。
noun · B2
Short trousers that someone has made by cutting the legs off a pair of long trousers, usually jeans. The word is always plural.
剪短的短褲
noun · B2
The act of stopping something completely, especially of stopping a supply of money, power, water or help.
切斷；中斷
以下是外部詞典記錄的用法，原文照列，我們還沒有寫成教學內容。上面的說明才是我們自己寫的；有些用法可能上面已經講過了。
cut-offadj
Having had shirt sleeves or pantlegs shortened by cutting material from the end.
這個拼法也被記錄為下列字的變化形：
資料來源：英文維基詞典 English Wiktionary（CC BY-SA 4.0）。 原文照列，未經改寫。