That should be possible. Download the video, might need something like Ummy video downloader to do that. It's a freeware program.
Once you've downloaded the video, open it up in Windows Movie maker or the apple equivalent and split the video at the start of the clip you wish to save and at the end also. Delete the bits you don't want and save the track you want to keep.
It might even be possible to do it using YouTube's editing program.
I'm on my phone atm but when I get on my pc I'll have a look at it.