Mobile Telephone Driving Safety Act of 2001 - Amends Federal transportation law to direct the Secretary of Transportation to withhold five percent of specified FY 2004 highway funds from any State that has not enacted or is not enforcing a law that prohibits the use of a mobile telephone while operating a motor vehicle, except in case of an emergency or other exceptional circumstance. Increases the withheld amount to ten percent after FY 2004. Allows such a State law to permit the use of a mobile telephone with a device that permits hands-free operation of the telephone if the State determines that such use does not pose a threat to public safety.