The Torah forbids ingesting the blood of animals. Human blood, according to Torah law, is not, strictly speaking, forbidden for consumption. However, the Sages enacted a prohibition against ingesting human blood due to the concern of "Mar’it Ha’ayin," meaning, that those who observe a person swallowing blood might mistakenly think that he ingests the blood of an animal. This prohibition applies only when there is indeed cause for such a concern, when onlookers might wrongly assume that the person ingests animal blood. But in situations where this concern does not arise, it is permissible to swallow blood.
For this reason, it is permissible to swallow one’s blood that has not left his mouth. For example, if a person’s gums bleed as he brushes his teeth, he is allowed to swallow the blood and does not have to make a point of expectorating the blood. Since the blood is still in his mouth, it may be swallowed. Likewise, if a person’s teeth or gums bleed while undergoing dental work, as long the blood never left his mouth, it may be swallowed. In these circumstances, nobody sees the blood – since it never left the mouth – and there is thus no concern of "Mar’it Ha’ayin."
However, if a person’s tooth or gums began to bleed while eating, and there is blood on the food outside his mouth, he must remove the blood or slice off the part of the food with blood. Since this blood has already left his mouth, it may not be ingested.
If a person has a bloody wound on his finger, he may, technically speaking, suck some of the blood from the wound (though obviously this is not advisable for other reasons). Since anyone observing him immediately recognizes that the blood he sucks is from his wound, and not from an animal, there is no concern of "Mar’it Ha’ayin." However, if the person had already bandaged the wound, and it is no longer bleeding, but he wishes to suck some residual blood from the area of the wound, this is forbidden. In this situation, it will not be evident to onlookers that the blood came from his wound, and it is therefore forbidden to ingest the blood in this case.
Summary: It is permissible to swallow blood from one’s mouth if it had never left the mouth; once it left the mouth, however, it is forbidden. Therefore, if one’s teeth bleed as he eats, he may swallow the blood in his mouth, but he may not eat the parts of the food that have blood on them. One may suck blood from a wound on his finger while his finger still bleeds, but one may not suck residual blood after the wound has stopped bleeding.