The easiest way to initially cut out your outline is to make a series of small cuts perpendicular to your art to create a series of thin tabs. Then, you break away those tabs with a pair of pliers. If a tab is too hard to break, go back in and cut it into two. In the more detailed areas, you'll want to make many thin tabs. You can also go back and tab areas after you've removed adjacent material.
The closer you can get to your final outline, the less work you'll have to do on the grinder.