The wounds of face bleed profusely because

Wounds on the face bleed profusely primarily due to its rich vascularity. The face is supplied by a dense network of blood vessels, most notably the facial artery, which is a major branch of the external carotid artery [t2, t4]. This artery, along with its terminal branches like the angular artery, provides an extensive blood supply to the facial muscles, skin, and organs [t6, t7]. In anatomy, the amount of bleeding following an injury is directly proportional to the vascularity of the affected tissue; more vascular structures naturally result in more significant hemorrhage [t8]. The facial soft tissue envelope contains a particularly high concentration of these vessels to support the complex functions of facial expression and sensory organs [t5]. While the face is relatively close to the heart, the profuse bleeding is a direct consequence of this high vessel density and the numerous anastomoses (connections) between them rather than proximity alone.

Sources

1. [1] https://www.ncbi.nlm.nih.gov/books/NBK536932/
2. [2] https://www.sciencedirect.com/topics/immunology-and-microbiology/right-common-carotid-artery
3. [3] https://pmc.ncbi.nlm.nih.gov/articles/PMC3589495/