The inquiry was prompted by the recent release of footage of a trainer kicking and punching a dog.
It also came just weeks after penalties were handed down in SA's first confirmed case of live baiting.
Premier Peter Malinauskas said the conduct in the video was unacceptable and animal welfare should be a paramount consideration for the industry.
He said a key question for the inquiry would be whether it remained appropriate for SA's greyhound racing sector to essentially regulate itself.
"There is a live question mark about whether or not that is an appropriate way for the industry to govern itself into the future," he said.
"Can it maintain the standards that this government and the broader community expect of them?"
Mr Ashton is due to report back to the government by the end of November.
He said he would conduct a range of interviews and consult broadly across the industry.
"The particular emphasis for me is on the welfare of greyhounds," he said.
"The footage in this case was abhorrent.Â
"It's really important that we examine how broadly this is going on and what other risks are out there to greyhounds and their welfare."
Greyhound Racing SA previously welcomed the independent inquiry and said it would cooperate fully.
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