PiedPiper, even with a separate small cutting mat it still makes me nervous, but you can use the corner of your regular mat or with extreme concentration and contortion of both yourself and your fabric, just make sure you are cutting through a single layer at a time. Yowza, I get tense just thinking of it.
I did a thread a month or two ago, and it was suggested that I get new scissors when I mentioned I was getting my best cutting from lower down the blade. You may not ever be able to use the tip of a given pair of scissors to cut smoothly with, just because of the leverage and the physical motion of the blades and the fabric -- but not all scissors are created equal. I certainly do need a better pair of applique/fine work scissors than I currently have even if I can get by for now with my larger pairs.
Like everything else, I first look at what I want to do, and then what are my options, and then what feels best to me. Whatever scissors feel best or are recommended by others don't matter if they don't feel right to you! And then I concentrate on getting the results I want, which doesn't always mean I get them how I want them. I want to take big 6" scissor cuts of my bias at a time... in real life with my actual current scissors I can only handle about 1.5-3" max smoothly at a time. I want smooth, I have a way to get it. And then I avoid the effort the rest of the time
