Aunt Annie's Crafts: Stick Puppets Cut out each puppet, taking care to stay close to the line around the puppet. If you printed on paper, a stronger puppet can be made by gluing the cutout to cardboard or cardstock. First do a rough cut, and then glue the puppet to a piece of cardboard. After the glue dries, finish cutting the puppet. The octopus puppet has two parts. How to Make Cardboard Puppets :: Creating My Cambridge 2. Cut out the black and white numbered pieces and stick onto your thick cardboard. Then cut out the shapes- these will form your main templates for cutting out your cardboard puppet. 3. Use the template piecies to mark and cut your pieces of (thinner) cardboard.