Is it a dog? Is it a cat? Is it a giant hole punch?

It stands in the corner of a studio – a large, solid, glossy-black plastic dog with a menacing grin – a maw which, seen in profile, reveals itself to be in the shape of a cat swallowing a mouse. This is the artist Noma Bar's latest project, an interactive machine that allows members of the public to feed different sheets of material into the jaws of the beast, and click down two buttons on its teeth to operate a form of giant hole punch, which will cut out an exclusive version of one of Bar's myriad designs.

As an object, it rather sums up Bar's work: with its bold, precise outline, the dog is playful but a touch sinister, while that mouse-within-a-cat-mouth-within-a-dog-mouth motif is typical of his ingenious graphic designs. Bar has long been interested in "negative space" – the name he uses to define his prints, which deal in witty visual puns, like old optical illusions brought bang up to date. So, what looks like a cut-out area is itself a picture, and together the negative, cut-out space and the positive space that surrounds it riff off each other, making meaning or forming a little narrative.

Of course, the very term "negative space" is itself a pun – while a lot of Bar's work has a dark side, or deals with the negative aspects of human behaviour. "I've been working with negative space over the past seven or eight years," he says. "It's there when I need it – when I need to tell a story, and add some more information."

For the interactive Cut it Out exhibition, at the Outline Editions gallery as part of the London Design Festival, visitors will be presented with a choice of 10 Bar designs to choose from. Some were originally designed on commission, others were inspired by objects glimpsed in Bar's own life – and it's fair to say he has an unusual way of viewing the world, an eye for these puzzled-together pictures. The way he sees it, "everything has two sides".

So, his piece Erotic Writer is both the nib of a pen and a woman's body, while Body Artist – the cover design for a short novel by the American author Don DeLillo – combines a man's face and woman's figure (the novella is about a dancer who still feels the ghostly presence of her husband). Night Train to London, showing a snoring man and a moon, was inspired by a real-life encounter: "I was coming back from Brighton to London and there was a guy sitting on the train next to the window. He was dribbling; very nasty, very drunk. But suddenly the train stopped by this rounded, neon light and it went from quite a nasty situation to quite a beautiful one; it seemed almost as though the moon was all around him, protecting him."

Born in Israel, Bar studied graphic design before coming to London in 2001 to seek his fortune with a student portfolio of Hebrew typography. Perhaps unsurprisingly, this didn't win him many job offers – but his knack at illustrating did. He sent samples of his work to various publications and received a good response. "A couple of weeks later I did a cover for Time Out, a Shakespeare with a question mark – 'To be or not to be?' – and I think that was my 'to be or not to be' moment as well, because I didn't really have time to do it!" Happily he found time, and it was soon clear that an artistic career was very much meant "to be". He has since illustrated newspapers and magazines around the world, held art shows in New York and Paris, and has just published his first book, also entitled Negative Space.

"I move along a fine line between design, illustration and art, which is a very interesting area, and I don't like to be pigeonholed in any of them," he says. "I love to do illustration, and I love the buzz of journalism, working with tight deadlines, and I love to work in the space of a gallery."

While his years training as a graphic designer have clearly been crucial, Bar had already been through his own equally influential "negative" space – compulsory military service in Israel. "From 18 to 21 I was a navigator in the Navy. [It's influence] is definitely there – I'm still dealing with these issues. I don't think a normal illustrator who hasn't been in the places I have been can handle political issues in the same way; I can understand exactly what journalists talk about."

Bar has been keen to move on from what he termed the "masculine culture" of the military, which he hated, and now takes pleasure in subverting. Discussing the hole-punch action of the big black dog – which seems to watch over our interview with its wicked smile – Bar suggests it is "kind of masculine too, the punching down. It's very not me, as a person, but I have fun playing with that. You have to put your hands inside the dog's mouth [to place in the paper], and I like that there is this little bit of danger almost."

Gallery visitors will almost certainly have fun, too. Playing around with it, we construct a print of his work Stalker in black leather and hot-pink paper, and I find the actual cutting process emits a satisfying a "ker-chunk" sound.

Although it seems a simple idea, for the metal die cutter – like a sharp cookie cutter mounted on a wooden board – to chop a shape out of a single sheet of A3 paper, a tremendous amount of pressure is needed: about 20 tonnes. Which means that doggy needs to be engine-powered.

It is a new process for Bar, too: he usually hand-draws his designs, scans them and turns them into a digital print. But Cut it Out, as he explains, "puts the texture back, it gives some kind of physicality, a tactile feel to it". He hopes people who choose their colours and cut-outs, who punch out and purchase the designs, will also feel some degree of ownership over them: as if the piece also features their own paw print.

The Cut it Out exhibition is at the Outline Editions gallery, London W1F, from 17 to 30 September, where visitors will be able to buy Bar's screenprints; they are also available at outline-editions.co.uk. Bar is running Create Your Own Cut-Out workshops at the gallery on 17 and 24 September, from 2pm to 5pm. To see a video of the machine in action, see above

Video credit: Crane.tv