Fresh off their worst season in more than three decades, the San Francisco Giants have taken a novel approach this winter to building a roster capable of returning to the playoffs: They’ve assembled a legitimate super team—from six years ago.

The Giants on Monday traded for outfielder Andrew McCutchen, a five-time All-Star, former National League MVP and one of baseball’s best all-around players with the Pittsburgh Pirates from 2012 through 2015. But after posting a .926 OPS over that span, the 31-year-old McCutchen has seen...