I believe this can be accomplished by using device specific dashboards. Have you tried using this feature in Tableau 10 then trying it on your mobile device?
If you're using Tableau 10.0, you can use the new Device Designer feature to create a dashboard that scales and adapts content depending on the screen size. See Diego's link above. However, if you're not using 10.0, I recommend doing the following:
- Create a dashboard using tiled layout instead of floating (it looks like you're already doing so)
- Change the sizing option to Automatic or Range from Fixed Size. Do so using the Size dropdown:
Automatic or Range will enable your dashboard to proportionally scales the dashboard to fill the embeddable space on the device screen or a blog.
If you're using Tableau 10.0: https://onlinehelp.tableau.com/current/pro/desktop/en-us/help.htm#dashboards_dsd_create.html?Highlight=device designe