Is bleeding from a cut or wound considered impure, and does it break wudu?

Blood is considered impure (najis) in all four Sunni madhabs and must be cleaned from the body and clothing before prayer if it exceeds a small, generally excused amount — but whether bleeding actually breaks your wudu is a genuine and well-known point of disagreement. The Hanafi school holds that blood (or pus) flowing out of a wound and spreading past the site of the injury does break wudu, based on their understanding of impurity exiting the body as a nullifier; the Shafi'i school (and largely the Maliki and Hanbali schools too) hold that bleeding from a cut or wound does not break wudu at all — for them, only discharge from the two private orifices, sleep, loss of consciousness, and a few other specific things nullify wudu.

In practice, this means someone following Hanafi fiqh who cuts themselves and bleeds needs to renew their wudu before praying (once the bleeding is cleaned up), while someone following Shafi'i fiqh only needs to clean the blood off their skin/clothing before praying and does not need to redo wudu, provided nothing else broke it. Either way, actively bleeding heavily enough that it can't reasonably be stopped or contained (a genuine medical excuse, ma'thur) has its own separate accommodation in fiqh, similar to chronic conditions like istihadha (see Q2).

Source: Hanafi position on bleeding as a nullifier of wudu vs. the Shafi'i position that it is not, per classical fiqh manuals of each school (e.g. Al-Hidayah for the Hanafi view; Minhaj al-Talibin/Shafi'i fiqh texts for the contrasting view).