Ralph Lauren Corp. is shaking things up—and cutting costs.

The company, which has been struggling with weak sales, on Tuesday said it would reduce corporate staff, close its Polo flagship on Manhattan’s Fifth Avenue, and move its online platform to Salesforce’s CommerceCloud solution.

The restructuring moves, part of the fashion retailer’s previously announced “Way Forward Plan,” are expected to result in annual savings of $140 million. They are on top of initiatives last year to cut costs by $180 million to $220 million.

The Polo store on Fifth Avenue is one of the company’s most high-profile locations. Its closing, scheduled for April 15, will leave…