I am unable to clear the screen of the mysql command line client like I know in case of java it is 'cls'.
In Unix or Linux you can use the:
Also you may try to use Ctrl + L in linux
However if you are using Windows then I think it is not possible. You may refer to this bug which is reported for the same for windows.
The only best think I can think of is you can only Exit MySql, Type
CLS and then re-enter MySql.