Yes, you can hide orders in a Completed status from the dashboard!
On the left side of your orders list/dashboard there are a many filters to help you find the orders you're looking for, fast. Look towards the bottom and you'll see the Filter by Status options, where you can choose to hide Completed orders. Click the eye icon next to "Completed" and a line will appear through the icon signifying that completed orders will not appear in the orders shown.
Please Note: The filters you set will save for you until you wish to change it or click Reset Filters.