In addition to being a red wine, claret is an old boxing announcer's euphemism for blood. In the good ol' days before televised fights, one had to turn on the radio and listen to the play-by-play without being able to see the boxers having at it. In order to keep things family friendly, apparently, when a boxer was bopped in nose one too many times and started to bleed, the announcer would proclaim something to the effect of, "Look out, folks, the claret has begun to flow!"

Sources:
Stephen King, Dreamcatcher
   (who says you can't read horror novels for their educational merit?)
http://www.thedailysports.com/extras/boxing/boxingextras/singlepage/blastfromthepast.htm
   (note the commentary from the second round: "...and Gulley put in another dreadful facer, which made the claret fly in all directions...")