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I'm working in Photoshop CC on a stamp type deal, and I'm trying to make certain lines that intersect disappear and retain transparency on the entire stamp.
Let me show you an example:
The part that I'd like to keep transparent, but overlap, is the box containing "CERTIFIED", including the text, I'd like the outer and inner rings to disappear when the box is on top of them, while keeping the box transparent on the interior.
You can use a knockout on the the box you want to "cut through"...
Give the shape an opaque fill (i.e. anything non-transparent)
Open that layer's Layer Style dialog...
Set Fill Opacity to 0%
Set a Knockout to either Shallow or Deep, depending on how far you want the transparency to go*
*A "Shallow" knockout will cut through to the end of the group the layer is in. A "Deep" knockout will cut through all the way to (but not through) the background layer.
A mask would work just as well, this gives you the benefit of being able to adjust the box without having to redo the mask every time though.
Use a vector mask.
Arrange it so that your ellipses are in a group, and the text and rectangle are above that group in the layers panel, and that the ellipses group is selected.
Using the Pen Tool, set to Path, and the option set to Combine Shapes in the toolbar along the top, draw two rough semi circles around the areas of the ellipses you wish to remain visible
Click Layer > Vector Mask > Current path
For example:
