Starbucks Corp. is putting its decadent Frappuccino on a diet, looking to reduce the drink’s high sugar levels, which have scared away increasingly health-conscious consumers and hurt sales.

Some versions of the drink contain more than twice as much sugar as a standard Snickers bar and far more calories. A 16-ounce Mocha Frappuccino contains 410 calories, compared with 250 in a 1.86-ounce Snickers.

It...