To remove transactions that the student isn't responsible for paying, you need to filter the Products and Billing items on statements then produce the statements separately for the Student and payer.

1. Make sure that you have the statements tab on the Student record set up as such:
Send statement to..                 Activity to show
Student                               All Transactions
Payer                                  Only the recipient's transactions
2. Go to Mail, Forms, and open the statement parameter you are working with or make a new one.
3. Select the Filters tab
4. The second to last row is Product and Billing Items on Charges
5. Access the drop-down in the include column and choose "selected"
6. On this page, set the filter for the product and billing items that only the student is responsible.  This depends how you have your product and billing items set up.  This could be one item or several.  You can choose individual items, a range of items or a query.  Choose what works best for your set up.
7. Click OK and preview the statement, for the student in question, it will only show the items that were chosen in the previous step.

NOTE: Unapplied Payments and Credits will still appear for multiple records.  Unused payments are not assumed to be applied to any specific record, so you must apply them or make sure the recipients know why they are seeing them on both statements