DES MOINES—Vermont Sen. Bernie Sanders aimed his sharpest jabs to date at Hillary Clinton, criticizing her evolving views, at a moment when the former secretary of state is gaining momentum in the race for the Democratic presidential nomination.

The polite tone of the Democratic contest took an unmistakable twist at Iowa’s Jefferson-Jackson dinner on Saturday, when Mr. Sanders, who entered the race vowing not to attack his opponents, painted Mrs. Clinton as someone who made the wrong choices for the wrong reasons on some of...