There are a variety of one handed cuts out there. Here I'll show you how to do a couple of them. They may seem hard at first but you'll be surprised how fast you'll be able to do them.
Practice for a while as you watch tv and you'll have them down in no time. But don't be surprised if you have to spend some time picking cards up. :)
We'll start with a basic one handed cut because it's the easiest. Then I'll show you one that's a little harder.
Hold the deck like you see in this image. All four fingers on the bottom edge and thumb on top edge. The deck is slightly angled toward your palm.
Allow the bottom half of the deck fall onto your palm. This part will take a little practice. If your hand isn't level the cards can fall off your palm.
Push the cards on your palm up with your index finger as you see in this image. Once the lower half is supporting the upper half. Let go with your thumb. The bottom half is holding the top half up.
Keep pushing up with your index finger until the edge of the lower half passes the edge of the upper half.
Then just let the half fall back aligned.
Here's a video of the cut in action. Practice. You'll get it.
This next one handed cut is a little harder. So practice over a tabletop. It'll be easier to pick them up then from the floor. :)
Hold the deck like you see in this image. Index finger on outer edge. Little finger on inner edge. Middle two fingers on lower edge and thumb at the inner top corner.
Lift the top half of the deck with your thumb. The upper half is supported between the index finger and thumb.
Continue to pivot the upper half with your thumb until it clears the lower half.
Then bring the half that started on top to the bottom of the deck.
Here's a video of this cut in action. Practice, practice, practice. If you get frustrated take a break and try again later. This is basically a form of juggling. It should be fun and relaxing.
Once you've mastered them. Play around with some variations. Such as this one I learned from a magician named Paul Harris. I need to practice this one more. Not quite as smooth as I want it to be yet.