Devi semplicemente specificare su quali tabelle applicare il DELETE .
Elimina solo il deadline righe:
DELETE `deadline` FROM `deadline` LEFT JOIN `job` ....
Elimina il deadline e job righe:
DELETE `deadline`, `job` FROM `deadline` LEFT JOIN `job` ....
Elimina solo il job righe:
DELETE `job` FROM `deadline` LEFT JOIN `job` ....