The Shareable Dashboard can't be directly downloaded, yet you can create a very similar report in terms of data and information, that can be downloaded.
You can choose to generate a PDF report from your Analytics or Mentions section. If you click on the download button, you'll be redirected to the Reports section.
The reports you create here can be downloaded as PDFs. Within your reports, you can add similar data to the one that you find within your Shareable Dashboard.