Formal:
* Bleeding: This is the most general synonym.
* Hemorrhaging: This is a more specific term for the act of bleeding.
* Exsanguination: This refers to the loss of a large amount of blood, often to the point of death.
Informal:
* Bleed out: This is a more informal way of saying "bleed to death."
* Gush: This describes a sudden and heavy flow of blood.
* Pouring: This refers to a large amount of blood flowing out of a wound.
The best synonym to use will depend on the specific context and the intended tone.