Using 'inverse / delete' with a smart object

Simply select the round area and click the add layer mask icon in the layers palette

As Michael mentioned,  you can't do that with a smart object, as it's it's own file. You can add a layer mask to cut out a section.

Generally speaking, a Smart Object can be thought of as another file contained within your Photoshop file. This "other" file may be embedded within your Photoshop file or it may even be stored on your hard drive or in the cloud within a library.

Double clicking the thumbnail of the Smart Object within the Layers panel will open up that file. You can then edit, save and close that file and your overall Photoshop file will update.

There are several Smart Object scenarios that potentially complicate the situation (such as vector content or embedded JPEGs) but that's the general idea.

Please fire away with any specific questions you might have. Cheers.