Flowing of blood from anywhere other than the private parts does not invalidate Wudu'
Does bleeding invalidate the Salah (Prayer)?
All praise be to Allah Alone, and peace and blessings be upon His Messenger, and his family and Companions.
We do not know of any Islamic legal evidence signifying that bleeding from any part of the body other than the vagina invalidates Wudu’ (ablution). The basic ruling is that it does not invalidate Wudu’. Acts of ‘Ibadah (worship) are Tawqifiy (bound by a religious text and not amenable to personal opinion), so no one is permitted to say that a certain act is an ordained ‘Ibadah, prescribed by Islam unless he has evidence. However, some scholars are of the view that excessive bleeding - according to convention - from any place other than the vagina invalidates Wudu’. Accordingly, it would be better in such a case that a person makes Wudu’ as a sort of precaution and to escape scholarly disagreement, because the Prophet (peace be upon him) said: “Leave that which causes you doubt and turn to that which does not cause you doubt.”
May Allah grant us success. May peace and blessings be upon our Prophet, his family and Companions