I used pre-painted plywood so I did four different cuts, however if you decide to paint after you cut then you can combine the logo text and yellow outline into the same cut to save time. The logo will fit in the center scrap left behind by the yellow portion.

The layers are rotated 45 degrees and sized so that they fit as big as possible on a 300x300mm piece of plywood. If you have a bigger machine then it should scale just fine.

If you didn't use pre-painted wood then you will need to paint the pieces from the different cuts. Don't forget that the centers of the letters A, R and P need to be retained and painted black.

You will also need to paint the teeth as they are to small and thin to cut from wood. I scored the outline of the teeth into the red layer and then painted them black with a fine tip acrylic paint pen. 

You could also cut the teeth from black vinyl and just stick them to the red as well. (if I make any more that's probably what I'll do)

Glue the layers together with red in the back, black in the middle and yellow on top. Once that is dry you can drop the white letters and black centers into the hole in the bigger black piece and glue those down as well. 

I used one of those saw tooth picture hangers right at the very top center. Just make sure the screws are less than 9mm which is the total thickness of the wood or they will poke through the front. You could also use a wire or even drill a small hole and use twine.