Here's a breakdown:
* "Mongrel" is a highly offensive and outdated term for a mixed-breed dog. In this context, it's a dehumanizing insult, implying Jacob is a savage and inferior being.
* "Watch yourself" is a warning, a threat of potential violence or harm.
Edward uses this phrase to establish his dominance and superiority over Jacob. He's trying to intimidate Jacob and assert his control over Bella, the object of their affection.
It's important to remember that the use of this word is highly problematic and reflects the series' problematic portrayal of Native Americans. While the author, Stephenie Meyer, has stated that she didn't intend to be offensive, the word itself carries a heavy historical baggage of prejudice and discrimination.