In a 1,270 word article on his website, the musician accused the north Shropshire MP of not being 'the sharpest tool in the box' and slammed his stance on issues such as the badger cull, fox hunting and gay marriage.
And he said the Cabinet minister had ignored a petition signed by more than 100,000 people last autumn by vowing to proceed with the two pilot badger culls in Gloucestershire and Somerset this summer.
TV star Oddie took to Twitter on Friday arguing that British wildlife was 'not safe' while Mr Paterson was in the high-profile cabinet post.
Mr Paterson told the recent National Farmers' Union conference in Birmingham that bovine tuberculosis was 'the biggest challenge facing us at the moment'.
He said the disease – which he said led to the slaughter of 26,000 cattle in 2011 – had cost the taxpayer £500m in the last 10 years, and that this could rise to £1bn in the next decade if the disease went unchecked.
But May, who was present at a hearing of the Government's Environment, Food and Rural Affairs select committee in the House of Commons this week, said opposition to the cull was gathering pace with nearly 200,000 people now backing the online petition.
He added: "The only hope is if the British public clearly say, with one voice – We will not stand for this.
"Owen Paterson himself is acting very smug, and grumbling about the fact that organisations like the Badger Trust have been 'slowing him down'.
"Well, that's democracy, Owen, though you don't like to hear it.
"And democracy ought to be strong enough to derail a hopelessly misguided policy such as this."
The global star also posted a link to his blog to his 87,000 followers.
But one person defended the Environment Secretary and tweeted back to Dr May: "What is 'unfriendly' about wanting to get control of an animal that is ravaging through the countryside spreading disease?"
And Mr Paterson today hit back at the latest remarks, saying he was using 'evidence and fact' to proceed with the plans.
"The evidence is there and there is nothing magic about this.
"We don't have a vaccine so we have to use all the tools at our disposal," he said.