The gopher was played by Fred Jenkins.
Harold Ramis looked into bringing in a live, trained gopher to act out the scenes, but Peters weasled some extra money out of the studio and tasked special effects supervisor John Dykstra (an Oscar-winning FX master who had worked on on Star Wars) to create a believable gopher puppet. This explains why Murray and the dancing rodent never appear together onscreen—the scenes in the gopher holes were shot by Dykstra after principal photography had concluded, and were cleverly stitched in to make the scenes appear seamless. The sound effects used for the gopher were the same sounds used for the dolphin in the 1960s TV series Flipper.