There are ideas and hacks how to use git, Mercurial or any other source version control system for this purpose. However, the LibreOffice XML format is not optimized for human readability, so tracking changes this way is tedious at best.
It seems that creating backup copies of your document whenever you would do a version control checkin, combined with the LibreOffice “Compare Document …” feature, works better. Because it is more comfortable: LibreOffice will show and highlight the changes within the formatted document, no need to read XML source. To use the “Compare Document …” feature, simply select that menu item from the “Edit” menu and then select the version to compare with. There is no need to have had the “Record Changes” function enabled during editing for comparing documents to work.
This assumes that you are the only author of the document. In case you work with collaborators, it has still to be evaluated if the LibreOffice “Merge Document” and “Record Changes” / “Accept and Reject” features (from the “Edit” menu) are more comfortable than a source version control system. But probably they are, except for some special cases.