Looking into the mySQL manual, there doesn't seem to be a function like that - it's not really useful actually either. You would either have to use a cron (attention, can be CPU intensive if you have it running too often!) or just put a check in front of your scripts to clear the old data ...
A check could look like this ... stop putting "1 hour" or something into the database, use a unix timestamp (get it with time()) - now if you want the table to expire in 1 hour, you'd get the timestamp in hour with a command like
$exp_time = time() + (60*60)
Now if you store this timestamp in the database (use BIGINT for the field type), you could put a command like the following on top of your scripts which would simply clear out all expired lines:
$result = mysql_query("DELETE FROM Table_Expire WHERE expiretime > " . time());
Hope this helps, best regards,
Bobbi