I was reminded more than once how much I hate sheers while making a long silk dress for a family wedding. Thankfully, I learned a trick which allowed me to make perfect straight-of-grain (straight line) cuts. Sorry, this doesn't work for curvy cuts, but it's perfect for anything that requires long straight cuts from one end of the fabric to the other (or from selvage edge to selvage edge) - like a shawl, or curtains.
Here's what you do. You make a little snip in the fabric where you want the cut. Then, you take a thread from the weave and you pull it until it is completely pulled out of the fabric - kinda like a run in your hose or something. What happens is that missing thread makes a line. Use it as a cutting line and you'll have a perfect straight-of-grain cut in a jiffy!
The fabric with gather a bit until the thread is completely pulled out.
If for some reason the thread breaks while you are trying to pull it out, just cut to the place the thread broke and pull another thread. Works like a charm. Perfect cuts make for less fraying...and less hair pulling all around. Good luck!