Hi,
Yes, you can clip their nails, but only the black part. The clear portion of the nail will bleed and is hard to stop if you cut it. Regular human nail clippers should work fine.
Also, you can replace their substrate with ceramic tile. This way, it will naturally file down the beardie's claws. As mentioned above, a rough basking rock would do the trick as well.
Believe me, I share your pain! Not nice looking like you own a feral cat, right?
-- Jacqui