You can connect a Blu-ray drive by USB or Firewire, or replace the internal Superdrive with a Blu-ray drive.
The graphics card has virtually nothing to do with video playback (other than displaying the images at specified fps). Your video decoding is done by the cpu. Even a 2 ghz Mini can handle Blu-ray playback, provided you have an efficient decoding application, such as Plex.
You need to tell us what the video's container is (e.g., m4v, mkv, etc.), its video codec (e.g., h.264 AVC, VC-1, etc.) and bit rate, audio codec (e.g. DD, DTS, etc), and if it has encryption or DHCP. Only then can we have a good idea if it'll play it.