My mom is in late stages of Alzheimer's, but her tongue pushes her food out. Suggestions?

If she is dying, she very possibly doesn’t want to eat.

Perhaps she is in the dying process and doesn't want to eat so she pushes out her tongue to stop from being force fed.
Or she can no longer chew and like already said her food needs to be pureed.
Either way I would be bringing hospice on board sooner than later.

You need to ask moms doctor to order a hospice evaluation stat. Mom needs pureed food since she's having swallowing problems. Offer her only puddings or ice cream for now. At 99 years old with advanced dementia, she's at end of life and needs comfort care.

I'm sorry you're going thru this. Best of luck.