I'm not sure about spiders but peppermint repels my daughter pretty fast.
If you breath enough peppermint, you get a little woozy and weird (I decided to rip out a strip that was about 10 x 40 feet one time). So maybe the spiders just get dizzy and wander off in a different direction.
Apparently it does work after a fashion - the spiders will only stay off the surfaces you treated and re-treatment will be necessary. So if you put your peppermint plant in the window sill, spiders won't walk on your peppermint plant but they will still be in your windowsill.
