There are a few point to remember when deciding how to cut patchwork.
One way is to make a pattern in the shape for the design, maybe a square, triangle, hexagonal or rectangle for example. Measuring out first on graph paper will ensure that the sides are equal and the diagonals go through the middle of the squares if drawing a hexagon.
This can then be cut out and the paper used as a pattern piece. If hand sewing patchwork then the paper is usually kept in the fabric until the item is nearly completed so quite a few paper patterns will need to be cut.
If the pattern is going to be used as a template, it can be transferred to cardboard so that it can stand being used over and over again tracing the shape straight onto the fabric.
If you are an expert in drawing and are confident to draw the shape straight onto the fabric then this is fine as well.
Another way is by using a cutting mat, cutting wheel and a wide quilting ruler. The mat is pre printed with horizontal, vertical and diagonal lines that along with the ruler enables you to cut the fabric out directly again making sure that the fabric is square before hand.
The mat should be larger than the fabric piece so the ruler can be lined up against the printed markings on the mat. The fabric is cut with the cutting wheel making sure pressure is put on the ruler to stop it from moving while cutting the fabric. The cutting wheel gives a nice clean edge and not jagged like it could be with scissor cutting.
I have found my mat invaluable, really pleased I bought it and it has been a pleasure to use. I bought quite a large one about 20 years ago, it is still good although slightly scuffed. The cutting wheel has kept sharp but alas the ruler has broken although I can and still do use the halves independently. These are good not only for patchwork but for cutting bias binding strips or tie fastening strips as well, practically any sewing.
Enjoy making your patchwork creations.