Before coming to the National Gallery of Art in 1980 as a Samuel H. Kress Pre-Doctoral Fellow, Grasselli was a graduate student at Harvard University and worked as a curatorial assistant in both the drawing department and the print department at the university's Fogg Art Museum. Grasselli has written and lectured widely on European drawing and printmaking with special emphasis on French master drawings of the 18th century and the art of Antoine Watteau and his circle. Prior to becoming a permanent member of the National Gallery's staff in 1984, Grasselli was the guest curator for the international exhibition Watteau, 1684–1721 (1984), which was presented at the National Gallery before traveling to the Grand Palais in Paris and Schloss Charlottenburg in Berlin.

Grasselli organized or co-organized several exhibitions for the National Gallery, including The Touch of the Artist: Master Drawings from the Woodner Collection (1995–1996); The Drawings of Annibale Carracci (1999); Colorful Impressions: The Printmaking Revolution in Eighteenth-Century France (2004); Private Treasures, Four Centuries of European Master Drawings (2007); Renaissance to Revolution: French Drawings from the National Gallery of Art, 1500–1800 (2009–2010); Italian Master Drawings from the Wolfgang Ratjen Collection, 1525–1835 (2011); and Recent Acquisitions of Dutch and Flemish Drawings (2016–2017). She co-wrote or co-edited the accompanying catalogues to those exhibitions and has contributed entries and essays to many other publications, both at the National Gallery and at other museums, most notably Mastery and Elegance: Two Centuries of French Drawings from the Collection of Jeffrey E. Horvitz (1998–1999) for the Harvard University Art Museums; Watteau and His World, French Drawing from 1700 to 1750 (1999–2000) for the American Federation of Arts; and Vernet to Villon, Nineteenth-Century French Master Drawings from the National Gallery of Art (2012) for the Fred Jones Jr. Museum of Art at the University of Oklahoma.

Grasselli received a PhD in 1987 from Harvard University. In 1989 she was the Ailsa Mellon Bruce Curatorial Fellow at the National Gallery’s Center for Advanced Study in the Visual Arts.