There seems no Linux tools to convert Visio document to SVG format, so I guess the only way is save as SVG using Visio itself. But is it possible to do it in command line?
You could also try vsd2svg, a commandline tool to convert VSD files into SVG ones: http://dia-installer.de/vsd2svg
According to this kb article, the only relevant thing you can do with Visio from the command line, is open or print a file. Both will result with a dialog box or an open document.
If you have a printer that can generate an SVG file (like the several ones that can generate PDF files you can get), maybe you could configure it as your default printer. Otherwise, you'll have to use macro recording tools to achieve this from the command line.