Yes, you can mass delete all answers in User-defined fields from the All Families menu. From the Families (menu) > All Families select multiple families in the 1st column you wish to update or leave the 1st column unchecked to select all the families. Click More (Mass Actions button)and select Clear UDF Answers.
You can mass delete the User-defined fields for ALL students at once from All Students. Go to Students (menu) > All Students leave the check box blank in the 1st column to select all students. Click the More (Mass Actions button)and select Clear UDF Answers.
The User ID must have the permission under Families to process a mass delete: Clear Family User Defined Fields and Family/Student Fixed Fees and Discounts.