My mom has advanced Alzheimer’s and her pet was put down, was I wrong to tell her?

On the down side, your mom was upset that her pet died. The upside is that she has something emotional and strong to engage her mind, as opposed to the daily mundane and boredom.
My mom's brother died last month. I didn't tell her fearing she would be too upset. But her sister told her. My mom cried the whole day. After that she was ok, just sad, but she was able to recall all the things she and her late brother said to each other before he died, and some stories from their past. She was sad, but her mind was engaged and got a good workout.

I agree with lindylu. I’m sure you did not take any pleasure in telling your mom her beloved dog had died. Nor did you do it on purpose just to hurt her. But, now that you’ve done so, absolutely use the therapeutic fib. I believe that in the moment, in that second, when you are speaking directly to them, people with Dementia do understand death and what it entails. That’s why they often react with denial and tears. However, a few minutes later, they have forgotten and once again are asking about the deceased one. And that’s why it’s best to use the therapeutic fib.

I think it was fine to tell her once, just to honor the relationship she had with her pet and for her to be able to say goodbye in her heart. But if she asks about it again, then I think it's ok to fib about it.

What's the point in telling her it's dead? What good does that do? Tell her it's out playing or at the groomer.

Pooh, when a person has advanced Alzheimer's chances are they will forget the news you told them rather quickly. Don't be surprised if Mom asks about her pet as though the pet is still alive. It is ok to use "therapeutic fibs" and say that the pet is doing fine, the pet is outside enjoying the weather, the pet is at the neighbors, the pet is at the Vet for a checkup, etc. Otherwise, Mom will mourn all over again.

I know this won't be easy since your Mom lives with you, thus the pet was in the house, correct?