How to clear cache automatically?

I turn on normal cache and set time interval to 10 minutes.
As i understand - now i also have to configure to run cron.php every 10 minutes.

I worry - can this slow down my site?

Maybe i can clear cache in other way, for example: when anonymous user visit page - drupal calculate "if cache is older then 10 minutes", if true - then cache is cleared.

Can i implement this mechanism of clearing cache?