How to make Mom stop being mean and talking nonsense?

Your mother sings?! As in "la-la-la can't hear you..."?!

That would make me fit to be tied!

Have you had any luck with arranging an assessment of her current mental state? Do you have any support with her care?

Thank you, mom sings when she is tired of hearing us disagree with her about her actions. If I respond to her that, no she didn't shower for a week, or she didn't take whatever is in her hands, she becomes angry. I have to stop reasoning and approach different ways. Thanks for the support and suggestions. I am aware that she is declining, she lives with me. She is still capable of so much that its frustrating.

She is 91 years old and you can't stop her at this age. Just ignore her when she talk nonsense...

Think brain damage. Different parts of the brain = different types of behavior. Some are memory, some are reasoning. Some are problem solving. Some parts of the brain are used for feeling safe, or memory, or knowing how to sequence. When you are a young child those parts develop as you are mature because your brain is still elastic. When you get a brain disease and you are older, you are not able to learn or process or even understand. It is not done on purpose, and rarely does anyone have any insight to know it is happening to them.
I hope this helps you understand your mother is not “being fresh”. She sees her behavior as perfectly reasonable. Everyone else is wrong and she is right.
Hugs, and know you are not alone.

Curing her dementia would be a good start, but no one knows how to do that yet.

Talking nonsense is what people with dementia do. It is one of the ways we know they have dementia. In certain situations you can work that nonsense into your requests. "You have a job? Mom, that is amazing! Not many people your age could handle that. If you are going to work you certainly will want to wear clean clothes. Let me help you out of those soiled pants."

Minimize the conflicts by minimizing what your tell her to do. Make sure the battle is worth it. (Many are not.) Limit yourself to what is absolutely necessary. For example, "Put your pajamas on" is not of the same importance as "wash your hands after using the toilet." And rather than telling her what to do, offer to help her with something. "Mom, would you like my help washing your hands, or would you rather do it yourself?" "Mom, I warmed your nightgown in the drier a few minutes. It will feel so cozy when you put it on!"

What kinds of things do you tell her to do that start her singing?

Unlike your children when they were young, your mother is no longer in learning mode. Meet her where she is, and don't expect what she is no longer capable of, like logical reasoning.

Your mother is further than mild Dementia.. She is acting like a child. You can no longer reason with her. She has lost that ability.