Exporting Visio drawings (*.vsdx) to XML vector graphics (*.svg) should be possible with Microsoft Visio using its default export function. You may also find 3rd party programs capable of the very same thing, however there are not that many utilities with support of Visio formats.
Convert Microsoft Visio drawing to XML based scalable vector graphics format.
We have found 4 software records in our database eligible for .vsdx to .svg file format conversion.
Microsoft Windows software - convert vsdx to svg on Windows
A versatile diagramming program
Convert from vsdx file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned vsdx to svg. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
A vector based diagramming software from Microsoft
Apple macOS / Mac OS X software - convert vsdx to svg on OS X
VSDX and VSD files viewer
Multiplatform software - convert vsdx to svg on any platform
A vector graphics editor