You don't need to cut out anything. It's much easier to do it the following way (I'm assuming you mean the portion on the outer edge where the tree shapes are barely visible):
1. Draw those zig-zags (Christmas tree edges) with the Pen Tool (choose shape)
2. Place your newly created shape over the red circle
3. Click and hold the Alt/Option key and move your mouse between the two layers (in your Layers palette). You should see an arrow showing downward. Click once and the new shape will only show the parts that are on the red circle.