A kind of paper where you can pull away the top layer?
While Elmy has the right idea with masking tape, I have found that, in practice, even the gentlest painter's tape tends to tear up paper.

What you want here is temporary repositionable adhesive (glue). It's available under a variety of brand names (Aleene's Repositionable Tacky Spray, Aleene's Tack-It Over and Over, Elmer's Craftbond Repositionable Glue, 3M Spray Mount Repositionable Adhesive, etc). These glues come in a variety of forms (spray, stick, and liquid) and function much like the line of glue on the back of a Post-It note--they hold in place, and peel away easily. Because of how gentle the glue is, it's very unlikely to damage paper when pulled away.

In a project like yours, you may wish to use a stick or stick and spray combination, to ensure you get enough adhesive around the edges of the cut-out to prevent glue from bleeding underneath. Cut the paper, run the glue around the cut edge, and follow the instructions on how long to let it dry before adhering it to your heavier ground, pressing along the cut edge to ensure it's as sealed as possible before giving it to the child to paint.