The seven-year-old won twice at the Cheltenham Festival for previous trainer Willie Mullins and finished third in the Gold Cup in March.
Along with Apple's Jade, another to disappoint on her first outing for Elliott, he had the highest profile of the horses Gigginstown House Stud removed from Mullins.
Reappearing in the JNwine.com Champion Chase on Saturday Don Poli was never travelling from an early stage and was pulled up by Barry Geraghty half a mile from home.
The race was won by Henry de Bromhead's Valseur Lido, another removed from the Mullins camp.
"He didn't want to go from the first fence so I don't know. I'd say Grand National but we'll get him home and see," said Elliott.