Take the needle plate off and see if there's anything caught in the cutter. The cutter parts can get bent, and the blade can get dull. Worst case scenario, you might need to replace the cutter.
Also, some threads are more springy than others. You could adjust the auxiliary tension (the small one above the main tension), tighter or looser. It holds onto the thread when the presser foot is up.
Make sure you're using good thread -- not "hand quilting" or "outdoor" or "buttonhole twist" or anything like that.
Good Luck to You!