There are different opinions on this depending on the different schools of thought. The opinions are as follows:
Hanafi School:
Blood that flows out of the body and spreads (i.e., beyond the wound site) nullifies wudu.
Maliki & Shafi’i Schools:
Blood does not break wudu, regardless of the amount, unless it comes out from the private parts.
Hanbali School:
There is some disagreement, but the dominant opinion is that blood does not break wudu unless it is excessive and intentionally removed (e.g., cupping).