Simplemente necesita especificar en qué tablas aplicar el DELETE .
Eliminar solo el deadline filas:
DELETE `deadline` FROM `deadline` LEFT JOIN `job` ....
Eliminar el deadline y job filas:
DELETE `deadline`, `job` FROM `deadline` LEFT JOIN `job` ....
Eliminar solo el job filas:
DELETE `job` FROM `deadline` LEFT JOIN `job` ....
