Not everything we do around here is something we put together ourselves--either from my head or from a book. Sometimes, I pull out a workbook. I love this Kumon Workbook for fun activities to build up paper cutting skills. It is for ages 2 and up. It is full of paper cutting activities designed to slowly build up your child's muscles, coordination, and cutting abilitly. It starts with simple, one-stroke cuts and works its way up to zig-zags and curves.
But you don't need to have the Kumon Workbook (or any other workbook) to do cutting activities. You can simply draw lines on paper for your child to cut. All you need are some child-safe scissors, a marker, and a piece of paper. Start with short, straight lines. Gradually make them longer. Move on to diagonal lines, zigs, zags, and curves.