My wife (67) is diagnosed with mild dementia and went to an attorney and filed for divorce, will a judge grant her the divorce?

If you are POA, that ends with divorce.
If you divorce, your wife will not have you to make medical decisions for her.
Then she will need financial assistance, bill paying. Does she drive?

How is your health? Do you know why she wants to divorce?
Have the two of you tried marital counseling?

Do you both, or does she have family to take over P.O.A. and her care.?
Can she live alone, or in assisted living right now?
Do you want to divorce?

This depends on her reason. I know a couple that divorced because he realized that in the years ahead his dementia was going to completely over take him, and he was protecting her assets from this financial catastrophe

Depends on the grounds, and whether or not Texas has no-fault divorce provisions. Also depends on the status of her dementia and whether or not she's cognizant of her actions sufficiently to understand the implications of divorce.

This is something that you'll need to address with a family or matrimonial attorney. Definitely don't get an estate planning or elder law attorney; they'll be out of their league. Divorces are a whole different practice.

You will have to answer the complaint, within the time specified on the Summons, and this isn't a DIY task.