The reason there's no "delete" function is because it would break a lot of things if people were to inadvertently delete students that were tied to past tournament results - the only way to ensure the integrity of tournament data is to make sure there's a stable student entry somewhere.
But, there's a simple workaround for your scenario. If you click the name of the students you don't want anymore on your Competitor Roster, and change their names to the same thing ("Harry Potter" or something), then you can use the "De-duplicate Students" function on the right side to merge all of those entries together. If 100% of those students have zero tournament entries/results, you can even merge them into a "real" student's name, and not be left with a dummy entry on your roster - since there's nothing to actually merge, it won't hurt anything.
There was a small bug last week that was preventing the de-duplicator from running - if that's still happening, let us know.