How can I remove all files in my git repo and update/push from my local git repo?

You could do it like this:

cd /tmp
git clone /your/local/rep  # make a temp copy
cd rep
git rm -r *                # delete everything
cp -r /your/local/rep/* .  # get only the files you want
git add *                  # add them again
git status                 # everything but those copied will be removed
git commit -a -m 'deleting stuff'
cd /your/local/rep
git pull /tmp/rep          # now everything else has been removed

There’s probably a oneliner for that…