Download the new Microsoft Visio Compatibility Pack
Visio 2010 users can use this pack to open files created in the newer Visio 2013 file format.
Visio 2010 users can download the Visio Compatibility Pack from the Microsoft Download Center. This pack lets Visio 2010 users open files created in the newer Visio 2013 drawing file format (files with a .vsdx and .vsdm extension). Be sure to check out the system requirements that are described on the download page. Looks like you’ll need to install Visio 2010 SP2, and some functionality in the pack requires the Microsoft Visio 2013 Viewer.
You can learn more about the new Visio file format in What IT Pros need to know about the new VSDX file format in Visio 2013.