This Help Center article will cover how to remove a vendor from the drop-down list on A/P vouchers, as well as remove them from the vendor area on a Purchase Order.  De-activation does not delete the vendor.  Any time a vendor has had financial activity, deletion is not allowed.  You can, however, remove the vendor from the drop-down list.  Only vendors with no financial activity can be deleted.  

Locate the Vendor record from the Vendor Module.  Once it is located on the Main Adress tab, mark the box in the corner of the record as removed from the list.  The vendor will be removed from the new A/P and PO drop-down list.