First you need to create a mock m_contractsDao and set it up. Assuming that the class is ContractsDao:
ContractsDao mock_contractsDao = mock(ContractsDao.class);
when(mock_contractsDao.save(any(String.class))).thenReturn("Some result");
Then inject the mock into m_orderSvc and call your method.
m_orderSvc.m_contractsDao = mock_contractsDao;
m_prog = new ProcessOrdersWorker(m_orderSvc, m_opportunitySvc, m_myprojectOrgSvc);
m_prog.work();
Finally, verify that the mock was called properly:
verify(mock_contractsDao, times(1)).save("Parameter I'm expecting");