{ "_id" : "750afe", "list" : [ "John@gmail.com", "Mike@gmail.com" ] }
{ "_id" : "711850", "list" : [ "example@gmail.com" ] }

DBCollection emailsApp = db.getCollection(EmailsInAppColl);
BasicDBObject queryEmail = new BasicDBObject();
queryEmail.put("_id", appId);
BasicDBObject updateEmailCommand = new BasicDBObject();
updateEmailCommand.put("$pull", new BasicDBObject("list", email));
emailsApp.update(queryEmail, updateEmailCommand, true, true);

DBCollection emailsApp = db.getCollection(EmailsInAppColl);
queryEmail.put("_id", appId);
DBCursor cursor = emailsApp.find(queryEmail);
System.out.println("######*****"+cursor.next());

#####*****{ "_id" : "711850" , "list" : [ "example@gmail.com" , "peanut@gmail.com" , "chewie@gmail.com" , "gold@gmail.com"]}

BasicDBObject match = new BasicDBObject("_id", appId); //to match your direct app document
BasicDBObject update = new BasicDBObject("list", email);
coll.update(match, new BasicDBObject("$pull", update));