The fullback and utility back, as well as versatile backrower Pete Samu, were the key omissions in a 34-man squad released on Thursday.
Injured co-captain Michael Hooper was named as part of a rehabilitation group in an indication he would be unlikely to suit up at the MCG against the All Blacks on July 29.
Wright has been a constant fixture of the Wallabies' backline in recent seasons and played fullback in the recent Rugby Championship defeats to South Africa and Argentina, while Hodge wore the No.12 against the Springboks but was not selected to face the Pumas.
Fit-again duo Andrew Kellaway and Jordan Petaia have effectively replaced Wright and Hodge, with both capable of playing across the back three.
Petaia has also played in the centres at Test level.
Izaia Perese and Lalakai Foketi are in the mix to replace outside centre Len Ikitau, who injured his shoulder while scoring against Argentina.
Taniela Tupou and Langi Gleeson, effectively replacing the reliable Samu, are also back in the fray after overcoming injury and could feature against the All Blacks at the MCG next Saturday.
Josh Kemeny, Matt Gibbon and Zane Nonggorr were the other omissions.
There was no room for playmakers Bernard Foley or James O'Connor, while Harry Wilson's barnstorming effort against Tonga for Australia A last weekend failed to win him a promotion.
"You're a professional sportsman, you get paid to do a job and if you don't do the job I guess you get left out," prop Angus Bell said of the shock exclusions on Thursday.
"It's week-to-week and if you have bad performance against the All Blacks, your position will be questioned.
"At the Wallabies level it's do or die. If you don't perform you don't get picked."
The Wallabies play again in Dunedin on August 5, with their subsequent Test not until August 28, against France on the eve of the World Cup.
Back-to-back losses since Jones' return have dropped Australia to eighth in the world rankings with just three Tests to play before their Cup kick-off against Georgia on September 10.
The All Blacks have powered to wins over South Africa and Argentina to lead the Rugby Championship.
But Jones, who coached the Wallabies to their last Bledisloe Cup series win in 2001 and beat New Zealand in the 2003 World Cup semi-final, can't wait.
"I quite fancy ourselves against New Zealand," he said on Wednesday.
"I don't think we've got any right to be confident. But ... if we're able to put a bit of pressure on them, which they haven't had this year, then funny things can happen.
"I like coaching against New Zealand. It's like the highlight of the year."
WALLABIES BLEDISLOE CUP SQUAD
Forwards: Allan Alaalatoa, Richie Arnold, Angus Bell, Pone Fa'amausili, Matt Faessler, Nick Frost, Langi Gleeson, Jed Holloway, Tom Hooper, Rob Leota, Fraser McReight, Matt Philip, David Porecki, Will Skelton, Blake Schoupp, James Slipper, Taniela Tupou, Jordan Uelese, Rob Valetini, Michael Hooper (rehab group).
Backs: Quade Cooper, Lalakai Foketi, Carter Gordon, Andrew Kellaway, Samu Kerevi, Marika Koroibete, Ryan Lonergan, Tate McDermott, Mark Nawaqanitawase, Izaia Perese, Jordan Petaia, Suliasi Vunivalu, Nic White.
Utility: Ben Donaldson, Dylan Pietsch
