For a remix, you would also need the permission to use the specific recording, (which can be declined) as well as rights from the song owner.
For example, If you wanted to cover Viva la Vida by Coldplay, you do it and pay the mechanical licensing fees. If you wanted to sample/remix it the recording of Viva la Vida, you would need to contact Capitol Records, who could decline or request specific payment. If you wanted to sample or remix the performance of Viva la Vida from Super Bowl 50, you would probably need the rights from CBS.
