One way to hold this word: something caught between two hard things and forced through — it comes out the other side still in one piece, but bent and crushed into a shape it should never have. That is the test. If it snapped in two, English says broke. If it is still all there and all wrong, English says mangled.
Wiktionary traces the verb to Middle English mangelen, from Anglo-Norman mangler / mahaigner, 'to cut to pieces' or 'to mutilate', and links it to mayhem. The word has meant 'forced out of shape' from the start.
Wiktionary 說這個動詞來自中古英文 mangelen，更早是盎格魯諾曼語的 mangler／mahaigner，意思是「切成碎塊、弄殘」，跟 mayhem 同一家。也就是說，「被外力弄得不成形」這件事，從一開始就寫在這個字裡了。
Wiktionary entry for mangle (verb, etymology 1), packet source_ref kaikki:3f6f69a190036ae4:753337921 — 'From Middle English mangelen, from Anglo-Norman mangler, mahangler... of Germanic origin, for which see mayhem.'
Three branches
東西被壓扭到變形
這一支就是核心畫面本身，作用在看得見、摸得到的東西上。
verb · B2
To damage something badly by crushing, tearing or twisting it, so that it loses its shape. It is also used about parts of the body that are badly hurt in this way, for example in a machine or a crash.
壓爛、扭壞
把聲音、句子或名字弄得面目全非
同一幅「被扭到變形」的畫面，只是這次被夾進滾輪的不是金屬，而是一首曲子、一個名字、一段程式碼。
verb · B2
To spoil a song, a speech, a name or a language by performing or saying it badly, so that it comes out twisted out of its proper shape.
糟蹋、唸得七零八落
兩根滾輪的那台機器
拼法和發音都跟上面一樣，來源卻不同。有趣的是畫面剛好對得上：東西被夾在兩根滾輪之間推過去。這是巧合，不是同一個字長出來的分枝，讀的時候當成兩個字比較安全。
noun · C1
A machine with two rollers and a handle, used before washing machines were common. You fed wet clothes between the rollers and turned the handle, and the rollers squeezed the water out.
絞衣機（舊式滾輪）