Cornyn, whose constituency is one-third Hispanic, said he was announcing his decision with "regret and some sadness," while acknowledging the political risk involved, according to the Associated Press.
"Voting to confirm Judge Sotomayor -- despite my doubts -- would certainly be the politically expedient thing to do. But it would not be the right thing to do," Cornyn said in a statement.
He added that many of her public statements "reflected a surprisingly radical view of the law."
Hatch said he will vote against Sotomayor because he disagrees with her judicial philosophy, even though he voted to confirm her appointment to a federal appeals court in 1998.
"Although Judge Sotomayor has a compelling life story and dedication to public service, her statements and record were too much at odds with the principles about the judiciary in which I deeply believe," he said in a statement.
The two Republicans join Senate Minority Leader Mitch McConnell (R-Ky.) and a handful of other Republicans who will vote against Sotomayor. A few Republicans in the Senate, however, have said they will vote to confirm the judge as the first Latina to sit on the high court, including Sen. Lindsey Graham (R-S.C.).