Greetigs from Sacramento CA. You are very brave for trying again. If it scares you too badly, you can get a pair of quilter's gloves. They give good traction and extra protection. I find that I MUST stand over the mat and look down at everything to get the best leverage with my cuts. (Both pressure on the ruler and pressure on the cutter)
If that still scares you, scissors can be used in quilting as well.
Be safe.