To cop a mouse was to come away from a fight with a black eye. It is one of the most vivid entries in J. Redding Ware's Passing English of the Victorian Era (1909), and Ware explains it with a lexicographer's straight face.

The cop is the verb you still hear in cop it or cop a look. Ware calls it a universal verb suggesting defeat or damage of some kind — to be caught, struck, scolded, found out or taken ill. In cop a mouse, he says, it means to catch or suffer.

The mouse is the bruise. In Ware's words: the colour of the obligation at its worst suggests the colour and size of the innocent animal named. A really good black eye, in other words, is about as dark as a mouse and about as big. The innocent animal is a nice touch: the mouse has done nothing to deserve this.

Ware files the phrase under Artisans' — the slang of skilled working men — and he gives no date or example sentence, so we do not know how long it lasted. Green's Dictionary of Slang lists it too, citing Ware alone.

It is a good example of how slang works. Nobody needs a word for black eye; there already is one. What the slang adds is attitude. I copped a mouse turns an injury into a story, and makes it sound almost like something you caught on purpose.