Final answer:
Sean Penn won Oscars for his performances in "Mystic River" and "Milk" in the 2000s, specifically in the years 2003 and 2008 respectively.
Step-by-step explanation:
The actor who won Oscars for acting in "Mystic River" (2003) and "Milk" (2008) is Sean Penn. Both performances were critically acclaimed and earned him the Academy Awards for Best Actor. In "Mystic River," Sean Penn portrayed the role of Jimmy Markum, a man entangled in a murder investigation, and in "Milk," he played Harvey Milk, one of the first openly gay elected officials in the United States.