Originally Posted by Yarn or Fabric

Rotary cutters are for cutting with rotary templates/rulers. The mylar or paper templates are for tracing, then cutting. Sadly if you are going to be using paper/mylar templates there is no quick trick.
There are lots of quilt units that you don't need templates for - like making half square triangles, etc. When I see a pattern calling for a unit that I know how to make without templates, I ignore the cutting instructions/templates and go about it my own way.