The Stats has to load and analyze every tournament in order to compute statistics. If you have a lot of tournaments and/or your tournaments are large and/or your PC is older or does not have a lot of memory (and/or a lot of other things, too), it may take a while to refresh the stats. I don't know what a long time means for you, but as an example I have a 4-year-old PC running Windows XP that takes about 3 minutes to refresh 114 tournaments. A different PC, much newer (a few months old) running Windows 7 with a lot more memory, refreshes the same tournaments in about 15 seconds.
Incomplete tournaments are not included in stats, so you don't have to remove/delete them. But if you'd like to, sure, they're just files and you can delete them. It might make refreshing your tournaments for stats faster if it doesn't have to load and analyze those tournaments. The Info dialog will give you the full path to the tournament file so you can delete it using Windows Explorer.