Mining and Minerals Resources Research Act - Authorizes to be appropriated to the Secretary of the Interior sums adequate to provide for each participating State $200,000 for fiscal year 1975, $300,000 for fiscal year 1976, and $400,000 for each fiscal year thereafter for 5 years, to assist each State in carrying on the work of a qualified mining and mineral resources research institute at one public college or university in each state. Creates an Advisory Committee on Mining and Mineral Resources to determine whether a college or university is eligible for assistance. Provides that Federal funds used to support research institutes must be matched by non-Federal funds. States that it is the duty of each institute to plan and conduct competent research in relation to mining and mineral resources and to provide for the training of mineral engineers and scientists. Authorizes to be appropriated annually for 7 years to the Secretary of the Interior sums to be made available to institutes to meet necessary expenses. Provides that $15,000,000 is authorized to be appropriated in fiscal year 1975, such sum increased by $2,000,000 each fiscal year thereafter for 6 years. Directs the Secretary to utilize the institutes to perform special research. Requires an annual report to the Congress by the Secretary of the receipts, expenditures, and work of the institutes under the provisions of this Act. States that nothing in this Act be construed to modify college-State relations or to authorize Federal control of education at any college or university. Directs the Secretary of the Interior to obtain the continuing advice and cooperation of Federal agencies and State and local governments concerned with mining and mineral resources. Requires the Secretary to establish a center for cataloging scientific research on mining and mineral resources. Sets forth the composition of the Advisory Committee on Mining and Mineral Research.