There is currently not a feature that allows you to remove jobs from your Available Jobs list under the Job Alerts button. However, there are a couple other ways to clear your list if interested:
1) You could reject the jobs on your sub-service's website (Aesop, SmartFindExpress, SubFinder), and the job will therefore clear from your 'available jobs list'
2) You could add filters to your SubSidekick site if you are repeatedly getting jobs for subjects or schools you know you're not interested in
3) You could add 'non-work days' or remove schools from your sub-service's website (Aesop, SmartFindExpress, SubFinder) so you don't receive alerts for days or schools you're not interested in