When the Spanish king Juan Carlos was taken to hospital at the end of last month, most mainstream newspapers and magazines carried endless coverage, analysing his latest operation in the finest detail.

Even the more leftwing media outlets weren't entirely sure how to judge the tone in a country which has an increasingly complicated relationship with the monarchy – once revered but now coming unstuck after a series of sexual and financial scandals.

The satirical magazine Mongolia was in no doubt how it felt. It published a picture of him on his deathbed, under the headline: "The last photo of the king." Except it wasn't a picture of the king, it was of Hugo Chávez on his deathbed. Except it wasn't actually Chávez – it was the same picture that left-leaning El País newspaper ran erroneously earlier this year, purportedly of the dying Venezuelan leader. When the picture turned out to be a fake, El País had to pulp an entire print run.

Thus Mongolia had lined up everyone in its sights: the king, the right, the left, and the press. The magazine's cover was a pitch-perfect spoof of the El País front page, down to putting an accent over the "i" in Mongolía, an in-joke much appreciated by readers. It summed up the monthly magazine perfectly – no one is safe from its jaundiced, critical eye.

Mongolia (so-called because the eight-year-old son of one of its co-founders liked the name) offers a vibrant mix of cartoon strips, spoof letters to the editor and bizarre, often psychedelic, graphics, all taking aim at Spain's more pompous institutions. But, like all good satire, its intent is deeply serious. Its back pages are called Reality News, and run under the slogan: "The part of Mongolia made up of real news – if you laugh from now on, it's your problem."

This month's edition contains a look at the controversial owner of La Razón newspaper, a report on one of former dictator Francisco Franco's more brutal torturers, and some scurrilous gossip in a section called Off the Record.Among the inspirations for Mongolia were Private Eye in the UK and the French magazine Le Canard enchaîné, and you can see their influence throughout its pages.

"We respect Spain so much that we don't respect it," says Gonzalo Boye, editor and legal mastermind behind Mongolia. Mongolia was born out of the financial crisis in Spain, a reaction to the recession, the ongoing corruption scandals, and what the Chilean-born Boye views as a craven press.

"There is no independent press in Spain," he said. "Newspapers are written to please, or annoy, powerful people, depending on who owns them. And there is no popular press – Spanish newspapers are not reader-orientated".

"If Mongolia didn't exist in a proper democracy you would have to invent it," says Boye. And so in 2012, a small group of disaffected journalists, cartoonists, and writers did just that. They took the concept to Boye, a garrulous, no-nonsense lawyer with a reputation for taking on complicated cases of economic and political corruption, because they knew the magazine would become a target itself.

"If people come at us, the magazine needs a lawyer like me." Thus far, not one case has been brought against them. They got some funding together, and built a wall between its financial backers and the editorial team: "No one tells us what to write," says Boye.

As a lawyer and senior legal partner, he had one piece of advice for his collaborators: "Just make sure your own back garden is clean."

And things are looking pretty good for Mongolia. The first edition came out in March 2012 but Boye says they now have anywhere between 20,000 and 30,000 readers a month, with 2,000 loyal subscribers, impressive in a country with a short tradition of a free press. It has a vibrant online presence, too, with more than 110,000 followers on twitter at the time of writing.

"We're happy where we are at the moment, but we want to grow, and we're thinking about going fortnightly at some point. We'll only truly be satisfied when every Spaniard knows we exist," he says.

Oh, and they send a copy to the king every month. They don't know if he reads it, says Boye, "but we'd like it if he took out a subscription".