If you need to re-save .vsdm files from Visio 2013 to older .vsd files, you will have to use the program itself, as no 3rd party program is known to use, that could otherwise handle this conversion. Simple File ► Save as.. should be enough.
Convert Microsoft Visio 2013 macro-enabled drawing file to Microsoft Visio diagram document.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert vsdm to vsd on Windows
A vector based diagramming software from Microsoft
Convert from vsdm file format
|Yes, Microsoft Visio supports vsd file conversion as a target file type.||Yes||Yes||vsd editor||Yes||No||No||No|
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.