Do I still need to mail a payment voucher if I chose direct debit?

No, if you are paying with direct debit then you do not need to mail in a payment voucher. 

What if it says I need to mail in the voucher in order for my return to be completed? Why would it say that when I did direct debit? Will my return still be complete if I don't send the voucher in when it says it is necessary to send it in on the Print/Save for your Records tab?

If you have paid using direct debit, you do not have to mail in the voucher. That would be something to keep for your records. @tentaigirl