There's a misconception that blood is blue when it is de-oxygenated, or without oxygen. This isn't true. Yes, blood changes its color a little bit when it is de-oxygenated but at no point is it completely blue in your body. When you look at your arm your veins seem bluish-green because the light that bounces off other tissues and skin make them appear that way. So, in space your blood would still be red if you got cut, it may be a different shade of red, but it will still be red.

If you had a cut out in space, just like if you were cut here on earth, your blood would be red. Your blood is always red. It can be different shades of red, but always certainly red. There is a myth out there that de-oxygenated blood is blue. This is in fact false. For more detail please see the answer to this question:

The blood with still be red, specifically the color of rust, which is the color that iron in blood makes when bonded to oxygen. The water in your blood would evaporate (indeed, boil), so it would look basically like boiling blood on a stove.