If you can find it, a 240g twill cloth will be much more stable and less likely to fray than the more common 200g cloths

Alternatively, a fine mist of spray tack on the cloth will help hold it together better. The stabilised fabrics like EC's pro-finish can be useful, but the edges will still be prone to fine fraying and you do lose a bit of drapability on moulds with complex curves

As mentioned already, you'll likely get cleaner cuts using something like an Olfa roller cutter too. With the addition of a little spray tack, you should find everything much easier to work with