America's Red Rock Wilderness Act of 1999 - Title I: Designation of Wilderness Areas - 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.

Title II: Administrative Provisions - Directs the Secretary of the Interior to file a map and a legal description of each designated wilderness area with appropriate congressional committees.

(Sec. 203) Provides that if State-owned land is included within a designated wilderness area, then the Secretary shall offer to exchange U.S. lands in the State of approximate equal value (prohibits the transfer of associated mineral interests) in accordance with the Federal Land Policy and Management Act of 1976 and the Wilderness Act.

(Sec. 204) Reserves the Federal Government's rights to a quantity of water determined by the Secretary to be sufficient for each wilderness area designated by this Act.

(Sec. 205) Sets forth provisions for the measurement of setbacks for roads with wilderness.

(Sec. 206) Permits authorized grazing of livestock within the designated wilderness areas to continue subject to such regulations and procedures as the Secretary considers necessary, as long as they are consistent with: (1) the Wilderness Act; and (2) the Arizona Desert Wilderness Act of 1990.

(Sec. 209) Withdraws such Federal land, subject to valid rights existing on the enactment of this Act, from all forms of: (1) entry, appropriation, or disposal under public law; (2) location, entry, and patent under mining law; and (3) disposition under all laws pertaining to mineral and geothermal leasing or mineral materials.

(Sec. 210) Authorizes appropriations.