ROME—Catholic bishops voted Saturday to water down a report earlier this week that advocated a significant shift in the church’s approach to gays and divorced Catholics, reflecting a deep split within the church’s leadership.

In a vote Saturday evening, an assembly of nearly 200 bishops, who have been discussing issues concerning the family at a special meeting known as a synod, took their final vote on a working document released Monday. That document, released halfway through the two-week synod, proposed a far more open...