Australian cricket captain Pat Cummins on Friday pulled out of the third Test against India after flying home mid-tour to spend time with his seriously ill mother.

Former captain Steve Smith will temporarily replace Cummins as skipper, with Australia scrambling to save face following two heavy losses in a nightmare start to the tour.

"I have decided against returning to India at this time. I feel I am best being here with my family," Cummins said in a statement.

"I appreciate the overwhelming support I have received from Cricket Australia and my teammates. Thanks for your understanding."

Cummins returned to Australia earlier this week citing a "serious family illness", but was initially expected to return to India in time for the third Test.

India hold an unassailable 2-0 lead in the four-match series after Australia lost the second Test by six wickets.

Talismanic opening batter David Warner was earlier this week ruled out of the Third test after suffering a concussion and an elbow fracture.

Veteran fast bowler Josh Hazlewood has also been scratched after failing to recover from an Achilles tendon injury.

Spin bowler Ravindra Jadeja tore through Australia's batting with figures of 7-42 during the second Test, as the visitors were bowled out for a dismal 113 in their second innings and lost by six wickets.

The third Test in Indore starts on March 1.