Mike Beebe's position on abortion was articulated by his spokesman in the course of an article in Saturday's Democrat-Gazette.
Asked whether Beebe favors further limits on abortions, Wright said Beebe personally opposes abortion and supports efforts to make it less necessary. Beebe “supports sensible restrictions like a ban on partial birth abortions and supports a strict law requiring parental notice for minors,” Wright said.
“The only exceptions that he supports are those required by the U. S. Supreme Court — rape, incest and life of the mother,” Wright said. “Mike Beebe believes this is a decision between a woman, her doctor and God.”
The U.S. Supreme Court doesn't actually require those exceptions -- the Roe vs. Wade decision only directs legislatures that would restrict abortions to provide exceptions for the "preservation of the life or health of the mother." Anti-abortion rights activists often say they would allow only the rape, incest and life exceptions to an overall prohibition of abortion.
So if those are the "only exceptions" he favors, Beebe is pretty much against the right to an abortion as it exists today.