I (and our local Access god) had to do this for a project a couple of months ago. We weren't just cloning the database, we were also changing the structure. He exported the tables to csv files, I wrote some perl to do things like translate the date, time, and boolean formats from MS to MySQL.
Because there isn't a perfect 1 to 1 mapping of data types between Access and MySQL, and we were restructuring the database, we found it easier just to csv export and then 'load data infile' into MySQL. You might also consider this route if your servers aren't network to each other.
The downside is you have to do this one table at a time...it would suck if you had 100's of tables :)