Thanks for your question. HIV transmission through blood exposure into a deep open bleeding wounds like you describe could happen in a situation like multiple injuries within a shared space as in a car accident. If a person with HIV is on medications which have reduced their HIV viral load to being undetectable, they cannot transmit HIV through their blood ( or sex fluids). Small wounds or cuts generally heal up quickly and would not be as risky an entry for HIV through blood. If you are concerned about about a particular incident, then consider getting tested for HIV now so you know your own status and at 3 months post the exposure so the test covers the window period.
Let us know if this does not answer your question or if you have any more questions or concerns.