> 1. run some javascript to generate the svg
You can have a build step, post build step, call another job, use the workflow plug-in, etc. The simplest would be to include a command that generates the SVG graph in your build, but there are many different ways to achieve the same result.
> 2. store the svg in the same URL as the previous build
If you archive your image as a build artifact. The URL won't change.
> 3. the description is updated in reload (the svg url doesn't change)
You can browse the configuration for that job for an example. Normally I use R to generate the graphs, but due to lack of time I decided to simply wget an image once and pretend I've generated it with some command :)
HTH
Bruno