Is versed sometimes used for arthroscopy of the knee or wisdom teeth removal?

Yes: Knee arthroscopy is usually reformed under general anesthesia and versed is commonly used with other drugs. In patients receiving conscious sedation for wisdom tooth extraction it is also a commonly administered medication.

Conscious sedation: Conscious sedation often uses versed or valium combined with fentanyl or Demerol (meperidine hydrochloride) to achieve a dreamy state where you relax ; often "forget." in this state, procedures as you describe can be comfortably performed. Talk with your surgeon/dentist as to whether he/she offers or recommends sedation.