Mitigation depends on the nature of the loss that might be suffered - and the answer is in your question: you do what is reasonable in the circumstances.
For example: Say the house flooded because the tenant did some dodgy home plumbing. Doing nothing about fixing the issue would potentially cause further damage by rot and mould. While the tenant may be liable for the flooding damage, it could be the landlord‘s duty to ensure it is rectified (and then charged on to the tenant) so that the water does not cause further damage. That’s mitigation, taking steps to prevent flow on or consequential damage or loss arising from an initial ‘injury’.