Bring a large pot of lightly salted water to a boil. Cook fusilli in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain and cool until running water. Drain and transfer to a large bowl.
Mix dill pickles, garbanzo beans, tomato, vegan mayonnaise, grape tomatoes, olives, dill pickle juice, fresh dill, dried dill, and dry mustard into the fusilli. Cover and refrigerate until flavors combine, about 4 hours.