Mincing is primarily used as an adjective meaning to be noticeably — and perhaps oddly or unnaturally — dainty or refined. You might remark, for example, on a lumberjack who takes mincing steps across a log, or a woman who speaks to her dog in a mincing voice. In these cases, the daintiness is unnatural — it's put on for show — or in the case of the lumberjack, so he won't fall off the log.