Hi Cinna!
Let me try to help. In the full version of Photoshop, there's no "cookie cutter" kind of tool, but are at least two ways to do this.
1. Choose the Ellipse Tool (in the Shapes tools) — hold down the shift key (to make sure it draws a circle not an oval) as you drag out a circle shape. Once the circle is the size you want, let go of the mouse first then the shift key. Position the shape above your paper layer and where you want the hole cut. Be sure the shape layer is active in the layers panel and then Ctrl/Cmd click on it to get the marching ants. Then select your paper layer and press the Delete key. That should delete the circle shape from your paper. Ctrl/Cmd D to remove the marching ants. You can delete the shape layer if you no longer need it.
2. Use the Brush Tool and choose a hard round brush, setting the size to what you want. Move your mouse to where you want the hole cut, then change the Blend Mode of the Brush to Clear. Stamp the brush down and you'll have a hole in your paper. Be sure to change the Blend Mode of your brush back to Normal when you're done.
Let me know if that helps, or if you were trying to do something else.