The number of U.S. taxpayers renouncing citizenship or permanent-resident status surged to a record high in the second quarter, as new laws aimed at cracking down on overseas assets increase the cost of complying and the risk of a taxpayer misstep.

A total of 1,130 names appeared on the latest list of renunciations from the Internal Revenue Service, according to Andrew Mitchel, a tax lawyer in Centerbrook, Conn., who tracks the data. That is far above the previous high of 679, set in the first quarter, and more than were reported...