Bono and his professional partner Lacey Schwimmer were eliminated from the ABC dance competition on Tuesday night following their tango performance on Monday.
Cher had previously criticised judge Bruno Tonioli's critique of the tango, which had included him describing Bono as like "a cute penguin trying to be a big, menacing bird of prey", and again voiced her annoyance at him and fellow judge Len Goodman on Tuesday.
Writing on her Twitter account after the result, she said: "I Have Got 2Hold my TEMPER ! MY Tears R OK ! Congratulations Chaz I'm SO PROUD OF U ! This was YOUR Quest...& u Followed your Star.
"But your mum "could cut a bitch" ! Thank u Carrie Ann 4 your Gentility u r beautiful inside & out ! To the Gentleman? I didn't know who u were b4 which I guess is a blessing ! Going Home is Fine but why insult him b4 he Goes!
"Maybe Rudeness & Flapping Arms take the place of TALENT ! As for the Older Gentleman ....every Show Needs A Grumpy Old Man !
"Condensed version ...The Chick is beautiful & Polite ! The Men suck."
> Digital Spy recaps Broadway night on Dancing with the Stars
> Chaz Bono, Lacey Schwimmer: 'DWTS judges comments rude, unnecessary'
Cher later added: "Needed 2 Vent ! It Would Have Been Blast if Chaz Stay-ed,But He NEVER Danced b4,so it was a Great Dream 4 a Great Guy!XX (sic)"
Bono and Schwimmer had scored 19 out of a possible 30 points for their tango on this week's Broadway-themed instalment of Dancing with the Stars.
Schwimmer had later voiced her annoyance at Tonioli's penguin comment on her own Twitter account, writing: "So proud [of] Chaz! He got under scored again, and tonights comments were the cherry on top.
"Having a judge refer to him as an animal every week is so rude and unnecessary."
She added: "I feel so bad about the comments week to week. It's not about the way someone looks, it's about the routine, the journey and dance. I am happy to be dancing with Chaz. #ANTIBULLYING."
Following the elimination, she took to her Twitter account to thank the couple's fans, writing: "Thank you all for the open minds and hearts for always supporting and being amazing human beings! You guys are all beautiful inside and out!"
Dancing with the Stars continues Mondays and Tuesdays on ABC