To mince is to chop into tiny bits. Your favorite soup recipe might include directions to mince four cloves of garlic.
When you dice an onion into very small pieces, you mince it, and when you grind meat very fine to make sausage or mincemeat, you also mince. Another meaning of the verb is to soften, or to express something in a gentle way: "She does mince her words when she talks to shy kindergarteners." The Old French root, mincier, means "make into small pieces," and it comes from the Latin word for "small," minutus.