As every Saturday Night Live season comes to an end, a handful of cast members learn they won’t be invited back for another year. For comedians who struggle to make their way into sketches, they can probably read the writing on the wall. But after one season in the mid-1990s, a number of the show’s biggest stars got the ax.

Dana Carvey, Phil Hartman and Mike Myers had already said their goodbyes, leaving the SNL spotlight focused squarely on Adam Sandler and Chris Farley. While young viewers worshipped the comics, older fans — and network executives — didn’t think the current cast was working out. Don Ohlmeyer, the NBC honcho who later pushed for the ouster of Norm Macdonald, first set his sights on Sandler and Farley, according to Lorne: The Man Who Invented Saturday Night Live.

“All the Baby Boomers, Don foremost among them, thought they knew...