Is Arthur's mother evil?

Few things here.

1. Arthur's mother didn't beat Arthur her boyfriend at the time did. You could say "why didn't she stop him" that's a more complex question than you might realize.
2. Mentally ill doesn't mean she's evil just might be a bit more likely to make poor decisions.
3. It's thought that the head injury may have caused his laugh, but the mother does say he was always smiling so never any confirmation.

Arthur's mother does seem to genuinely care for Arthur though she seems like she was quite a poor mother early on, but evil, no, just a representation of a poor troubled environment that may have led to Joker.

It is also possible that she was telling the truth about the Father and was trying to get money to help herself and Arthur.

But later, it is revealed that she was mentally ill and she abused Arthur, causing him a head injury that in turn caused his incontrollable laugh.

It is not clear she was mentally ill at that point or even at all, an alternative view could be that Thomas Wayne used his power and influence to have Arthur's mother committed to a psychiatric hospital and the adoption papers forged to discredit her if she ever tried to make it public that Thomas Wayne is the farther. This may have even caused her mental illness.

There is a scene where Arthur holds a picture of his mother when she was much younger and he finds an inscription on the back of the image "i love your smile -TW".

This suggest to me that Arthur's mother was telling the truth about their relationship.

Brett Cullen, the actor who plays Thomas Wayne said to the Hollywoodreporter.com

"The backstory was that Arthur’s mother had worked for Thomas in his home, and she was a beautiful woman who Thomas was attracted to and it led to a physical relationship," Cullen says of his conversations with Phillips. "Later in life, she’s in and out of mental institutions. And in my mind, Thomas Wayne put her there." hollywoodreporter.com