How to store count value in DB
in your case you will have to repopulate the order column completely
because if you delete row id 118 or 119, you need to change 118,119,120 and so on till the end of table

so in this case i suggest the following using the ROW_NUMBER() function 

    update YourTable
    Set [order] = NewOrder
    from 
    (
    SELECT t.id,t.[order],@rownum := @rownum + 1 AS neworder
  FROM YourTable t, (SELECT @rownum := 0) r
    ) X
    where YourTable.id = X.id


so in this case if you delete 118

Delete from YourTable where id = 118


run the above update script again and then you will see that your order field is updated

Select id,[order] from YourTable