The only ones I can remember from when I was a kid are Cassandra Cain, who was nearly mute until she had a lot of speech therapy (and it took her a few years to decide she wanted it), and some 'hilariously' crazy comic relief types like Snowflame. As far as I can tell those people no longer exist in the new 52, and I wondered if this was a systematic thing or if they just aren't in the books I read.
DC's New 52 has almost no examples of characters with non-neurotypical disabilities. While no official mandate has been voiced, we have noted character changes correcting flaws from the previous continuity. (Not saying DC's universe had many such characters but now there are none.)
Black Manta - the only character officially mentioned with autism in the DC Universe. It is not known if the autism aspect of the character was kept with the reboot of the DCnU.
A second origin was given in #8 of the 2003 Aquaman series. In this origin, the boy who would become Black Manta was an orphan who has autism and was placed in Gotham City's Arkham Asylum. He felt comfortable in freezing cold water, while cotton sheets were excruciatingly painful.
Because the attendants at Arkham did not know how to deal with autism, they would end up restraining him to the bed as he struggled and screamed whenever they tried putting him there. The boy was also fascinated when he saw Aquaman on television.
The boy would end up being subjected to experimental treatments. One treatment seemed to clear the boy's head, but left him violent as a result; he killed the scientist who had administered the treatment and escaped from Arkham.
Cassandra Cain - formerly mute and unable to speak as part of a developmental training issue from her father. All of her communication skills were redirected into her combat abilities. After therapy, she had limited communication skills and became more social. It is unknown how much of her previous origin remains intact in the DCnU.
Cassadra Cain served as Batgirl. Cassandra's backstory presents her as the daughter of assassins David Cain and Lady Shiva. She was deprived of speech and human contact during her childhood as conditioning to become the world's greatest assassin.
Consequently, Cassandra grew up to become an expert martial artist while simultaneously remaining mute, developing very limited social skills, and being illiterate.
Barbara Gordon - after being shot and paralyzed by the Joker, Barbara Gordon's career as Batgirl ended and she became the information broker Oracle. In the DC reboot, a cure is found for her condition and she returns to her Batgirl persona.
Amada Waller - Also known as 'The Wall' she was the lead government operative in charge of the government operative unit known as the Suicide Squad. In the previous DCU, she was a larger, obese woman who has been transformed into a younger and more physically perfect specimen. While this does not quite meet your question of mental disability, it does show another example of DC's quest for physical perfection for its characters.
Autism and other non-neurotypical conditions are rarely shown in the comic medium due to its heroic mythic nature. Such characters fall out of the range of the genre and are rarely seen as heroes. Cassandra Cain was an extraordinary exception.