Can I mass delete information that is filled in under a Student's User-defined fields?

Yes, you can mass delete the User-defined fields for ALL students at once from the Students menu > Clear UDF Answers.

Additionally, you can delete all answers in User-defined fields from All Students.  Go to Students (menu) > All Students and select the students in the 1st column with a checkbox. Click the More (Mass Actions) icon and select Clear UDF Answers.

The User ID must have the Students permission Clear Answers in Student User-defined Fields (UDF).