cut up rough behave in an aggressive, quarrelsome, or awkward way. British informal
☞ Cut up is here being used in the sense of 'behave'. The phrase cut up rough is used by Dickens and the variant cut up savage (now no longer in use) by Thackeray.
2007Telegraph Mr Miliband wants to prove a point to Mr Brown-who cut up rough with him over details of the Climate Change Bill, blocking his idea for personal carbon budgets.