The Arduino serial monitor isn't a regular terminal so its not possible to clear the screen using standard terminal commands. I suggest using an actual terminal emulator, like Putty.
The command for clearing a terminal screen is ESC[2J
To accomplish in Arduino code:
Serial.write(27); // ESC command
Serial.print("[2J"); // clear screen command
Serial.write(27);
Serial.print("[H"); // cursor to home command