Hi Torstein,
Unfortunately this won’t be too easy at the moment. To do it you’d need to modify /wp-content/plugins/the-events-calendar/views/table-mini.php by placing a copy in an ‘events’ folder in your theme and then changing the query to use WP_Query instead of tribe_get_events() so you can use tax_query args and limit the categories. This is likely going to have impacts to the rest of the code in the file and this is where it gets tricky.
We are working on some changes to allow for more flexibility in our queries but this probably won’t be out until 2.1 which will be a couple/few months.
I hope that helps!
– Jonah