Computer Shuts Down While Watching Blu-Ray DVDs

The first thing that springs to my mind is that your computer might not be able to handle the data transfer required to watch Blu Rays so it overheats and shuts down. Is it an old, low spec pc that you recently added a Blu Ray player to?
Another thing could be that your graphics card or monitor can’t handle Blu Ray resolution. Can you try increase the resolution or try another graphics card?
The first thing I would do is upgrade the drivers for the Blu Ray player, Graphics card and Blu Ray player software and see how you go.