This is easy with a query:
select source, alias from url_alias INTO OUTFILE '/tmp/url_aliases.csv' FIELDS TERMINATED BY ',' ENCLOSED BY '"' LINES TERMINATED BY '\n';
If you are good with mysql, you can run this directly from mysql with your drupal database selected.
If you are using drush you can run the query this way from the command line when in your site's root directory:
drush sqlq "select source, alias from url_alias INTO OUTFILE '/tmp/url_aliases.csv' FIELDS TERMINATED BY ',' ENCLOSED BY '\"' LINES TERMINATED BY '\n';"
If you have the developer module installed, you can run this with db_query in /devel/php:
db_query("select source, alias from url_alias INTO OUTFILE '/tmp/url_aliases.csv' FIELDS TERMINATED BY ',' ENCLOSED BY '\"' LINES TERMINATED BY '\n';");
You can also run the above code anywhere in the code base that runs on page execution, and then remove it once you have gotten your csv.