The new Google Places dashboard was missing an important feature, the ability to delete or remove a business listing from your dashboard. But as of last night, Google has enabled that feature in the new places dashboard.
Jade Wang from Google announced it on Google+ saying, "remove a listing now available for new Places dashboard users."
Users of the new Places dashboard can now remove listings from their accounts (http://goo.gl/SwxLvO). Please note, you cannot undo removing a listing from your account.
If your business is closing, make sure you first report it as closed using Report a Problem (http://goo.gl/lGwPSS). If you'd also like to remove the business from displaying in your dashboard, first access the dashboard for the business you wish to remove. Select the Gear icon, then select Remove this listing.
Note that Google may continue to show businesses that have been removed from your account on Google Maps, Search, and other Google properties as closed, moved, or open, depending on the information we’ve received about the business.
I should note, this feature was available and is still available in the old places dashboard. The first image is of the new dashboard, with the gear box that allows you to "remove this listing" and the second image is of the old dashboard where it says "delete" next to the listing.