Complex sentence: When the Westerns folded, he moved on to the New York Mutuals, and played the rest of the 1875 season with them, as well as the entire 1876 season, when the team moved over to the new National League when the Association folded.
Split into simpler sentences: When the Westerns folded, he moved on to the New York Mutuals and played the rest of the 1875 and the entire 1876 seasons there. The Mutuals then moved over to the new National League when the Association folded.