"Yes, we are parting company just basically over fees, I imagine. I just put up my fees for the first time in 10 years and Gigginstown chose not to pay them," Mullins told At The Races on Wednesday.
"Everyone who comes into my yard is treated the same," added Mullins, Ireland's champion trainer for the last nine years.
"I see enough people going to the wall in Ireland all the time and we've evolved our methods of training, which obviously costs a lot as well, and we are not prepared to sacrifice that."
Gigginstown said in a statement that the decision had been made with "considerable regret" due to the increase in fees.
"We hope that an agreement can be reached at some time in the future which will allow Willie to resume buying and training more graded winners for us," it added.
Irish media reported that Mullins would lose around 60 horses as a result of the split, including Don Poli, third placed in the Cheltenham Gold Cup, and Ryanair Chase runner-up Valseur Lido.
"There's a fantastic team of horses going to whoever's going to get them, I don't know where they are going to go," said the trainer, who said they would be hard to replace.
"It's all only been in the last few hours that this has come about. I wish them the best. It's the way it is. We just move on, I think."
O'Leary, the chief executive of Europe's biggest budget airline, has horses at a number of Irish yards including those of Gordon Elliott and Mouse Morris.
Don Cossack, trained by Elliott, won the Cheltenham Gold Cup for Gigginstown in March while O'Leary's Rule The World, saddled by Morris and ridden by Mullins' nephew David, won the Grand National at Aintree in April.
(Reporting by Alan Baldwin in London, editing by Ed Osmond)
