How to remove local git history after a commit?

I would like to switch from Dropbox to the open source Sparkleshare. It uses git for the syncing and versioning. If say I had a 1GB file I deleted in my folder, it stays within the history of the local .git folder. But I would like to have this kind of heavy data on the server and not the client. How can I commit my repository and delete the local one with git? Many thanks!