First, you need to stabilise the fabric underneath so when you are cutting your pattern pieces the fabric doesn't slide around. This can be done a few ways.
In this example, I'm using tissue paper pieces.
Lay your pressed fabric on top of the tissue.
Pin your pattern pieces through fabric and the bottom tissue.
Pin goes all the way through.
Cut along your pattern edge, cutting through all layers - fabric & tissue.
Pro: It's quick & easy and hold fabric really well.
Con: You are using fabric cutting scissors to cut paper!
Another option is to cut only the fabric layer like above, leaving the bottom tissue paper layer intact.
Not as quick & easy as the first method but will save your scissors.
Another option is to use a pressed cotton bed sheet instead of tissue (great for larger pattern pieces). Pin all three layers and only cut your fabric layer like in the image above.
Ensure you are working on a hard, flat surface. Trying to cut slippery or any fabric for that matter, on carpet will end in grief!