If you are working with commercially made blu ray, you'll need a decryption program. You can get the trial for AnyDVD HD and run it in the background to break encryption and try to cut clips out with something else, but I'd recommend ripping the entire thing to the hard drive and work from there.
Two other choices for decryption would be MakeMKV and DVDFab.
To cut sections out...there's the rub. There aren't too many good editing choices for blu ray, since you might be looking at VC-1, H264 or Mpeg2 in blu ray. All are valid choices for encoding blu ray video. H264 is the most common of course.
You could try Avidemux 2.6 for cutting out clips. Make certain that you are cutting on I frames. And set the program to Copy for Video and Audio. You'll need to save as mp4 or mkv files. And when you make a name for the resulting file, make certain to give it the appropriate file extension....for example if you are making an mkv, name it something like Avatar clip.mkv. And test each clip to make certain you don't have audio/video sync problems.
You could burn to dvds if you want. Burn as data if your player can handle mkv or mp4 files. Burning them to dvds doesn't turn them into dvd-video. That would be an entirely different format and would require conversion. You'll need a blu ray player though, as a simple dvd player cannot play back HD video off a disc.