Cutting a small piece of a video and saving it

So I'm looking to make a highlight reel more or less of some gameplay footage. I have 15 minutes of gameplay that I recorded, but I really only want to cut out several 10 second or so intervals of that gameplay. I know that I can simply click on the scissors at the time stamp I would like to cut from and click on them at the time stamp I would like it to stop from, but how do I then just save that snippit as it's own clip? I can't seem to extract it from the source video