I suppose if the only problem is the 'suction' of the oil later, then a lever with a pin through it would do. The lever would reach under the edge of the vice through a T slot, with a pin through it to provide leverage against the table. This could break the vice away from the table an allow it to be picked up.
Alternatively, use a T bolt or similar held in the vice and <something in the spindle>. Either lower the table or raise the head, as appropriate to the mill. Then a bit of wood can be slid under the vice and it can be released from the spindle and hauled out of the way.