Elsom has been struggling with a strained ligament in his foot and his fitness will be reassessed before the Wallabies leave for South Africa on August 15.
Mortlock's recovery sees Ryan Cross drop to the bench, with recent rugby league convert Timana Tahu missing out altogether just a week after making his international debut.
Queensland Reds' back row Hugh McMeniman takes Waugh's spot among the replacements.
Australia currently top the Tri Nations standings with nine points ahead of their first away tie of the competition following wins over South Africa (16-9) and New Zealand (34-19) on July 19 and 26 respectively.
However, the All Blacks have won the last seven encounters between the two sides on New Zealand soil, with 2001 also the last time Australia have recorded back-to-back wins over their neighbours.
Graham Henry's men will be defending a 22-year-unbeaten run against Australia at Eden Park in Auckland, a venue where the All Blacks completed a 3-0 whitewash of the Lions with a 38-19 victory in 2005.
Australia (vs New Zealand, Saturday, August 2, Auckland)
15. Adam Ashley-Cooper (Brumbies)
14. Peter Hynes (Queensland Reds)
13. Stirling Mortlock (Brumbies, captain)
12. Berrick Barnes (Queensland Reds)
11. Lote Tuqiri (NSW Waratahs)
10. Matt Giteau (Western Force)
9. Luke Burgess (NSW Waratahs)
1. Benn Robinson (NSW Waratahs)
2. Stephen Moore (Queensland Reds)
3. Al Baxter (NSW Waratahs)
4. James Horwill (Queensland Reds)
5. Nathan Sharpe (Western Force)
6. Phil Waugh (NSW Waratahs)
7. George Smith (Brumbies)
8. Wycliff Palu (NSW Waratahs)
16. Tatafu Polota-Nau (NSW Waratahs)
17. Matt Dunning (NSW Waratahs)
18. Daniel Vickerman (NSW Waratahs)
19. Hugh McMeniman (Queensland Reds)
20. Sam Cordingley (Queensland Reds)
21. Ryan Cross (Western Force)
22. Drew Mitchell (Western Force)