Drag and Drop file to desktop when windows are maximized

Solution 1:

You have several possibilities:

1. Use the sidebar and drag & drop files or folders on the 'Desktop' item
2. Create a 'Desktop' Dock item by dragging and dropping the folder '/Users/YourUserName/Desktop' to the Dock and afterwards drag & drop files or folders you want to move on the 'Desktop' item in your Dock
3. Create an Automator Service to move (or copy) chosen items to the 'Desktop' folder (rough example)

Solution 2:

In addition to klanomath's answer:

You can also assign a Hot Corner to show the Desktop. In that way you can drag a file to the Hot Corner, the Desktop shows, then drop the file on the Desktop. Move your mouse to the hot corner again to show the original window.

The Hot Corner functionality can be found in the Desktop & Screen Saver System Preference pane.

Solution 3:

You can also use Keyboard Shortcut to show Desktop while dragging the files. Default shortcut is: ⌃ CTRL+↓ DOWN ARROW (User look suggests also CMD ⌘+F3).