You can picture something turning fast, and a piece leaving it. The piece is not thrown away — it lands, stays whole, and starts moving on its own. Two details carry all three meanings. The piece began as part of something bigger, and it now has a life of its own. Whether the piece is a side character, a department of a company, or a useful result nobody planned for, the same thing has happened: it came off the main turning body and kept going.
The noun comes from the phrasal verb spin off. The verb is the movement; the noun is the piece that came off.
這個名詞是從動詞片語 spin off 變過來的（來源寫的是 deverbal from spin off）。動詞講的是「甩出去」這個動作，名詞指的是「被甩出去的那一塊」。所以英文寫法也分家了：動詞是兩個字的 spin off，名詞才是 spin-off。
Wiktionary entry supplied in this packet (source_ref kaikki:3f6f69a190036ae4:1387417151): 「Deverbal from spin off.」
Two branches
分出去，自己站起來
這一組裡，甩出來的那一塊會變成一個獨立存在的東西：一部新作品，或一家新公司。它跟原本的主體還看得出親戚關係，但從此自己走自己的。
noun · B2
A new show, film, book or game built out of a part of an earlier one — usually by taking a character from it, or keeping the same world, and giving that piece its own story.
衍生作品
順手甩出來的好處
甩出來的那一塊，這次不是一個組織，而是一個結果。你本來在做別的事，它自己飛出來，而且剛好有用——這一支把重點從「分出去的東西」換成「意外得到的好處」。
noun · B2
A useful extra result that falls out of work done for some other purpose — nobody was aiming for it, but it turns out to be worth having.
附帶成果