to make an ostentatious display or forceful impression
See swath in American Heritage Dictionary 4 Idioms
cut a swath
To create a great stir, impression, or display: “He cut a bold and even sacrificial swath across American politics”(Gail Sheehy).
To extend in distinctive physical length and width: “the surprising 17th Arrondissement, which cuts a generous swath across northwest Paris”(Jean Rafferty).