Both men have been released on bail.
The dump in Kidlington, between the River Cherwell and the A34, is thought to contain approximately 21,000 tonnes of waste in a pile which is up to 150m (490ft) long and 6m (20ft) high.
The mound of rubbish is made up of what appears to be processed domestic waste, shredded plastics, polystyrene, tyres and other household items.
It is just one of 517 illegal dumps across England, at least 11 of which contain more than 20,000 tonnes of waste. They include a 280,000-tonne site in Cheshire, two 50,000-tonne sites in Lancashire and Cornwall and a 36,000-tonne tip in Kent.
The total number of such larger sites is likely to be higher, as the Environment Agency has previously told the BBC it does not hold data on tonnage for every illegal tip.
Most sites are in countryside locations, often hidden, and on what should be agricultural land.
Police say many are run by organised crime gangs, who are making cash by charging much less than legitimate operators to take and bury waste.
Businesses have to pay site fees to use legitimate licensed landfill sites, depending on the amount and type of waste they are trying to get rid of, and landfill tax is also charged at just over £126 per tonne.