To mince something is to chop it into very small pieces, smaller than what you would get by chopping or dicing. The pieces should end up 1/8 inch (30 mm) or less in size.
At home and in restaurants, vegetables are minced with a knife, a blender or a food processor.
Meat is minced commercially using special machines.
History Notes
Machines for mincing meat were invented in Britain in the 1870s. In 1885, the Eastbourne Board of Guardians in London ordered a mincing machine in order to prepare meat for those in their care who didn’t have teeth. Before that time, meat could of course have been minced by repeating chopping in home kitchens, but wouldn’t have generally been available commercially.
Literature & Lore
Mince also means to “walk daintily”, as in saying that someone “minced down the street.” That kind of mincing usually requires either significant heels on your shoes, or shoes that were meant for another gender’s feet.