SAN DIEGO—Mitt Romney’s advisers begged him not to go to war with Donald Trump. After he decided to go ahead, Mr. Trump dismissed him as “lightweight” and “failed candidate.” This week, Newt Gingrich called him “pathetic.”

Mr. Romney, sticking to his guns, has become a rare figure in American history—a former presidential nominee openly defying the man succeeding him as his party’s standard-bearer.

Sitting...