Connecting to one Mac from another shows shared drives that no longer exsist
On the Mac Mini, you will want to open up the Sharing Preference Pane and go ahead and delete all the shares that you wish to no longer have listed.

The changes should be immediate, but I suppose the other computer that connects to the shares might need to log out and in if you are still seeing phantom entries.

Also, there is a slight case your Airport hardware is proxying these shares in case the Mini goes to sleep, so you might want to just shut down the Mini, then the router and finally the MacBook if you can't get these entries to clear.