Significant Transnational Criminal Organization Designation Act This bill makes membership in a significant transnational criminal organization a ground for inadmissibility into the United States and provides for criminal penalties against those that provide material support to such an organization. The bar against admission applies to an alien member of such an organization and an alien spouse or child of such an individual. The bar shall not apply to a spouse or child who (1) did not know, or should not reasonably have known, that the individual was a member of such an organization; or (2) has renounced the organization in question. The bill establishes statutory authority and procedures for the Department of Justice to designate an organization a significant transnational criminal organization. The Department of the Treasury may require U.S. financial institutions to block transactions involving assets belonging to such an organization. An individual who knowingly provides material support or resources to a significant transnational criminal organization (or attempts or conspires to do so) shall be fined, imprisoned for up to 20 years, or both. If the death of any person is the result, the offending individual may be imprisoned for any term of years or for life. A financial institution that becomes aware that it possesses or controls funds belonging to such an organization shall retain such funds and notify Treasury.