What kind of a shout can be called mincing?
[
Her laughter, her gestures, her assertions became more violently
affected moment by moment, and as she expanded the room grew
smaller around her, until she seemed to be revolving on a noisy,
creaking pivot through the smoky air.

“My dear,” she told her sister in a high, mincing shout, “most
of these fellas will cheat you every time. All they think of is
money. I had a woman up here last week to look at my feet, and when
she gave me the bill you’d of thought she had my appendicitis out.”
]
ch.2
http://xroads.virginia.edu/~hyper/fitzgerald/gatsby/gone.html

Question

What kind of a shout can be called mincing?
[
Her laughter, her gestures, her assertions became more violently
affected moment by moment, and as she expanded the room grew
smaller around her, until she seemed to be revolving on a noisy,
creaking pivot through the smoky air.

“My dear,” she told her sister in a high, mincing shout, “most
of these fellas will cheat you every time. All they think of is
money. I had a woman up here last week to look at my feet, and when
she gave me the bill you’d of thought she had my appendicitis out.”
]
ch.2
http://xroads.virginia.edu/~hyper/fitzgerald/gatsby/gone.html

Answer

Although Sunny has given a fairly modern definition, I understand (given the rest of the text) that ''mincing'' should be understood in the same manner as literally mincing meat. Or maybe a sound like the grind of a mechanical mincer.

Answer

Mincing describes the actions of someone who acts dainty or refined.