I already developed my web app and published it to azure with asp.net core 1.1 and it was working fine until I upgraded my web application to Core 2.0 final
With a bit of searching this worked for me.
Essentially clean out the wwwroot folder from a console on your Azure Portal. Make sure you get the top most wwwroot folder (I had a sub wwwroot folder for some reason.)
RD wwwroot /S /D
Should do the trick. Then just republish your site. It would appear that the publish process does NOT delete anything that already exists within the deploy folder. So you have 1.1 .dlls and 2.0 .dlls.
Hope that does the trick for you.