America's Red Rock Wilderness Act of 2001

America's Red Rock Wilderness Act of 2001 - Designates specified lands in the following areas of Utah as components of the National Wilderness Preservation System: (1) Great Basin wilderness areas; (2) Zion and Mojave Desert wilderness areas; (3) Grand Staircase-Escalante wilderness areas; (4) Moab-LaSal Canyons wilderness areas; (5) Henry Mountains wilderness areas; (6) Glen Canyon wilderness areas; (7) San Juan-Anasazi wilderness areas; (8) Canyonlands Basin wilderness areas; (9) San Rafael Swell wilderness areas; and (10) Book Cliffs and Uinta Basin wilderness areas.

Sets forth administrative provisions regarding: (1) filing by the Secretary of the Interior of a map and a legal description of each designated wilderness area with appropriate congressional committees; (2) the exchange of State-owned lands within such areas; (3) Federal reservation of water rights; (4) measurement of setbacks for roads with wilderness; (5) authorized livestock grazing; and (6) withdrawal of such lands from disposition under certain public land laws.