Key to cutting out the tricky fabrics is to make sure that the weight of the fabric is supported, ie if you cannot fit all of it on your cutting area, make sure the excess is well supported so that it does not drag on the main part that you are cutting. Then use lots of pins, LOTS of pins, placed horizontally in the seam allowance and cut in a single layer. If it is a very fray-y fabric, I would also consider increasing the seam allowance as well (eg 1.5 to 2cm).