If someone is brain dead and on a breathing tube why would they perform dialysis on their kidney?

Brain death: If a patient is declared brain dead, there is no use for hemodialysis. Hospitals usually stop all therapeutic procedures on such patients along with having the patients have their breathing tubes removed.

Organ Donation: If the patent is truly "brain dead" and not just in a coma, the only reason to continue artificial breathing and dialysis would be if the patient's other organs (heart, lungs, liver) might be able to be harvested and used for organ donation.