"How the hell would her utterly irrelevant musings represent an appropriate evaluation to the world of the state of the Wallabies."
But other journalists jumped to Newman's defence, saying Jones' singling-out of the female reporter was unnecessary.
Sports writer Roy Ward tweeted: "I feel utter disgust at Alan Jones even speaking Beth Newman's name. There is only one 'mouthpiece' in this discussion and it's the bloke who thinks using the N word on radio is proper conduct."
The tweet alluded to Jones' use of the colloquial phrase "n****r in the woodpile" last week in reference to the Liberal Party leadership spill.
Jones apologised for using the phrase the next day on 2GB radio.
Another sports reporter told Jones to "get a life" for a "completely out of line crack" at Newman.
Others questioned Jones' decision to single out a female reporter in his column.
Sports reporter Christy Doran said: "Sure, attack Rugby Australia and the system. But why bring one of our female colleagues into your weekly column?"
Newman has worked at rugby.com.au since September 2015, having previously worked as as sports reporter at the Brisbane Times.