You can't sew without dealing with cut threads. I've tried several methods to keep my threads in one place until I accidentally came across my favorite. I am a knitter, too, and one day I had a swatch I had knit in order to figure my gauge for a sweater project. I reached across the yarn swatch to place my threads in another spot, and the yarn almost grabbed the thread. I have used this ever since then. I don't have to shake my fingers. I just go close enough for one bit of the thread to touch the yarn and it sticks. It is also very easy to clean. Once it gets full, I hold it over a trash can and pull all the threads off in one motion.
Another method comes from Tea of Tea Quilting. I saw on one of her videos that she pins a piece of batting to her shirt front while using her longarm. It works just like my yarn and holds the threads in place. Combining my idea with Tea's, I am thinking I will knit a small heart or some favorite shape and pin my yarn on when I am using the longarm.
What is a fantastic method you have found to keep your threads in one place?