1
general::
Absent oneself from a class or other, usually mandatory event, as in If he cuts one more class he'll fail the course. [Late 1700s]
American Heritage Idioms
2
general::
Phrase(s): cut class [and] cut school
to skip a school class or a day of school without an excuse. • As a joke, one day all the students cut their math class and went to lunch. • Jane was grounded after she cut school last Friday.
McGrawhill's American Idioms And Phrasal Verbs