The woman said within a month of her 12-year-old daughter signing up to the site she was asked to provide naked pictures of herself, told to kill herself and called a whore and slut.
She looked at her daughter's friends' profiles, and in three days found two children threatening to kill themselves in response to abuse on the website.
One, a 13-year-old girl, was sent violent pornography depicting a rape, was challenged to fights and was told, "I am outside your house watching you" at night.
"How a 13-year-old copes with all of that I just do not know, it gave me bad dreams for a few nights. The horrifying thing is you can send pornography in video or picture form, and there is no way to know what you are going to open."
She said she took screenshots of the worst abuse and reported it to ask.fm, but has had no response after six weeks.
She is working with other concerned parents from Britain - where the suicide of a 15-year-old was linked to ask.fm in April - to target the website's advertisers.
Ask.fm has more than 40 million users and is based in Latvia. A spokeswoman said content was monitored constantly and processes were in place to help prevent antisocial behaviour.
"We are committed to providing a fun, informative and safe service for our users - so we urge users who witness or experience unpleasant behaviour to report it to us immediately by clicking the 'report' button."
Genuine complaints were swiftly acted upon, she said.
NetSafe chief executive Martin Cocker said ask.fm was "saying the right things, but they are yet to be doing the right things".
"We should be clear that ask.fm doesn't advertise themselves as having a particularly safe environment."
Staying safe on ask.fm
*NetSafe recommends that young users of ask.fm prevent anonymous questions being posted by choosing "do not allow anonymous questions" in their privacy settings.
*It is possible to block an abusive user after receiving a second message from them, by pressing "block" next to each question.
*Users can also use a "report" button to notify the site of abuse.