There isn't a way for students or instructors to clear answers to an activity and "start over from scratch." However, this isn't a problem!
Students: As long your instructor hasn't closed the assignment, any changes you make are saved automatically, and your instructor will always see the most recently saved version of your answers. If you would like to start over from scratch, simply delete all of your answers manually.
Instructors: As long as an assignment is set to Accepting Responses, students can edit their work. Their work is automatically saved any time a change is made, and you always see the most recently saved version of their work. If a student would like to start over from scratch, they will need to manually delete all of their answers.
One exception to this are locked sections.