Grylls took over the WA National party this week. He proposed the tax the day before doing so, as part of "new ideas" to improve the state's finances, the Sydney Morning Herald reported.
The tax would generate around $3 billion a year from mining companies BHP Billiton and Rio tinto, the Sydney Morning Herald said.
A BHP Billiton spokesperson said: "We are concerned about the damaging proposals flagged recently in the media in relation to an additional tax on BHP Billiton and Rio Tinto. Stable government policy is vital for the economic security of WA and the nation. We do not understand why a proposal that is so discriminatory and uneconomic would be targeted at two companies."
"More than 90% of the state’s royalties come from iron ore. BHP Billiton has paid AU$65bn in taxes and royalties in Australia over the past 10 years, including AU$10.6bn in royalties to the WA government. In addition, BHP Billiton has invested over AU$25bn into the Pilbara over the last decade.
"Miners in WA are operating in an international market and we have to be able to compete or [we will] lose market share. BHP Billiton wants to grow our contribution to WA and the best way of doing this is to make sure it remains a great place to invest and do business," the spokesperson said.
Rio Tinto said in an emailed statement that it is "one of Australia's largest corporate taxpayers and has paid record royalties of almost AU$11bn to the WA government since 2010. This has been on top of our AU$52bn spend on local goods and services over the same period."
"There are no grounds for a new mining tax in WA," it said.