I don't know why but the image you posted, while it doesn't show up in the reading view, if you click on it, it does actually open. The distressed look is not going to be easy to recreate at the size needed for a mug, I'd suggest not even trying, just do the font without the distress. The steps to auto trace this in inkscape are as follows;
1 - open png image in inkscape
2 - In Inkscape, select image, then click Path->Trace Bitmap
3 - the default settings should work well enough for this image.
A few notes, outside of the diamonds this is all text and would be best to recreate it rather than trace. The diamonds are just straight lines so I'd redraw those rather than trace. If you do go the auto trace route, the white of the logo goes out to the very edge of the image, that'll cause some issues when autotracing. Edit the png image first to add a bit more black around the edge so that the white doesn't touch the edge.