I am going to play devil's advocate here (with brettd), mostly for fun, to argue that the Slaughterhouse Case overturned the Dred Scott ruling. Further, it might be helpful to begin with what the Dred Scott ruling actually WAS.
Dred Scott vs. Sandford was an important court case held in 1857 where the United States Supreme Court ruled that African Americans (it didn't matter whether they were slaves or free people) weren't citizens, couldn't sue others in court, and further, that the government couldn't regulate slavery in the new US territories.
Of course, what is really important is that, after the Civil War, the 14th Amendment DID give African Americans citizenship, allowed them to sue, and gave them protection "under the law." Brettd is right when he says that it is THIS amendment that truly nixed the Dred Scott ruling. It was just swept under the rug for a while by the conundrum of citizenship (saying that Dred Scott was not a citizen of the United States).
The fact is, though, that until the Slaughterhouse Cases, the Dred Scott decision was still in effect! Therefore, we have to say that those cases directly overturned the Dred Scott vs. Sandford case due to its result.
No Supreme Court case following the 1857 Dred Scott ruling directly overturned the decision of Justice Roger B. Taney's court, however, the 14th Amendment, following the Civil War, gave equal citizenship to freed slaves following abolition, and promised them "equal protection under the law".
This, the 14th Amendment directly overturned that part of the ruling which argued that the federal courts had no jurisdiction in the case because Dred Scott was not a citizen of the US, but merely the citizen of a state. The 14th redefined citizenship, thus overruling any state laws on citizenship requirements.
Some historians have argued that the Slaughterhouse Cases re-interpreted the Dred Scott case by reiterating that the 14th Amendment was designed specifically to overturn the 1857 ruling, but this was simply emphasizing the earlier amendment's meaning and importance.