Beale's omission allows former rugby league international Hunt to make his first appearance for the Waratahs after leaving the Queensland Reds under a cloud in the wake of two arrests for drug possession in three years.
Ashley-Cooper, 34, returns to the light blue of New South Wales after three years in France as he bids to play in a fourth Rugby World Cup in Japan later this year.
Coach Daryl Gibson said leaving Beale out of his side was part of a policy of resting Wallabies from Super Rugby matches to reduce the risk of burnout for Australia's top players ahead of the World Cup.
"Karmichael's inclusion allows us the ability to manage the workload of Kurtley, who was the Waratahs highest minute player in 2018," he said in a news release.
"KB will get an extra week to prepare for the season ahead. This is a new approach for Australian rugby teams, rotating players and managing their worldloads leading into a World Cup campaign.
"This is why we ensured we had depth in our squad so we have the flexibility while remaining competitive."
Two players look set to make their Super Rugby debuts for the Waratahs when the 2014 champions host the 2016 title winners on Saturday.
Prop Rory O'Connor, 24, and 22-year-old lock Lachlan Swinton have been named on the bench for the clash at Brookvale Oval, where the Waratahs will play some of their home matches while the Sydney Football Stadium is redeveloped.
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
