The showbiz matriarch sent the 'Bad Romance' star an open letter after she failed to ask her fans - who are known as 'Little Monsters' - to stop sending threatening messages to Sharon's daughter Kelly after she poked fun at the singer's outfit at the 2012 Grammy Awards on her clothing critique TV show 'Fashion Police'.
Instead, Gaga published an open letter to Kelly in which she criticised her for choosing ''a less than compassionate path'' by working on 'Fashion Police', prompting Sharon to hit back and accuse her of condoning bullying.
In the letter, Sharon wrote: ''Ms Gaga, Your open letter is full of contradictions. You are nothing more than a publicity-seeking hypocrite. I am calling you a bully because you have 32 million followers hanging on your every word and you are criticising Kelly in your open letter. Are you so desperate that you needed to make this public?
''A word from you would stop all the hideous, negative, and vile threats from your little monsters.''
Sharon was particularly furious because Gaga has spoken openly in the past about her own struggles with bullies, and even has a charitable organisation, The Born This Way Foundation to help victims of bullying.
In an extract from her autobiography 'Unbreakable', which is being serialised by The Sun newspaper, she wrote: ''Gaga's the self-proclaimed poster child for anti-bullying.
''By not repudiating her fans' bullying, she was condoning it. That's why I called her a hypocrite.
''I was so disappointed because I had always been a huge fan. But you can't bang on about being anti-bullying and then refuse to tell your fans to stop haranguing other young women with nasty threats.
''On Gaga's last tour there would be a bus at each venue and she put therapists in there for kids who were bullied.
''I felt it was just a publicity stunt. Perhaps the next time she has one of these mobile counselling stations she should go in and ask the therapist for advice on setting good examples for her fans.
''Gaga may have been bullied at school, but she was also a rich kid that got everything she wanted. She should know better.''
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.