Criminal Alien Gang Member Removal Act This bill makes non-U.S. nationals (aliens under federal law) associated with criminal gangs inadmissible for entry into the United States and deportable. The bill also establishes procedures to designate groups with criminal gang status. An individual shall be inadmissible if a consular officer, the Department of Homeland Security (DHS), or the Department of Justice knows or has reason to believe that the individual is or was a criminal gang member or has participated or aided such a group's illegal activities. An individual who is or was a member of such a gang, or has participated or aided such a group's illegal activities, shall be deportable. Such individuals must be subject to mandatory detention. Furthermore, such individuals shall not be eligible for (1) asylum; (2) temporary protected status; (3) special immigrant juvenile visas; or (4) parole, unless they are assisting the government in a law enforcement matter. The bill defines a criminal gang as a group of five or more persons (1) where one of its primary purposes is committing specified criminal offenses and its members have engaged in a continuing series of such offenses within the past five years, or (2) that has been designated as a criminal gang by DHS. The bill also establishes procedures for DHS to designate a group as a criminal gang, including notifying Congress, publishing a notice in the Federal Register, and providing an opportunity for the group to petition for administrative and judicial review of the designation.