[{"_id":"123","name":"ABC","elements":{"_id":"123","minorElements":[[{"id":"xyz1","name":"xyz1"},{"id":"xyz2","name":"xyz2"},{"id":"xyz3","name":"xyz2"}],[{"id":"xyz1","name":"xyz1"},{"id":"xyz3","name":"xyz2"}]]}}]

db.collection.aggregate([{"$project":{"elements.minorElements":{"$filter":{"input":"$elements.minorElements","as":"item","cond":{"$not":{"$in":["$$item._id",["xyz1","xyz2"]]}}}}}}])