Note: Please see @Pekka’s answer for the Windows version, which seems to be that there is none for windows. However, this is a useful post to take a look at for windows. The remainder of this answer shows how you can do it in Unix / Linux and exists for historical significance as it has clearly been useful to some users.
To clear the editor screen in Unix/Linux you can type:
system clear
This makes use of mysql’s system command to call the shell’s clear command.
Note: the system command works only in Unix.