The government is cracking down on visa overstays by international students and exchange visitors with a new policy that changes the way they’re penalized for violating the terms of their visas.

The new policy memorandum from U.S. Citizenship and Immigration Services changes the way the agency calculates “unlawful presence": time in the U.S. that counts against a foreign national who may wish to leave and return legally. Remaining in an unlawful presence for too long can prevent someone from entering...