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Create a square document.
Fill the background with black
Create a new layer and fill it with white
Use Free Transform to rotate the white layer 45°
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Using the same general idea, you could do this on any aspect ratio image by making a square selection centered on the image, and use Select > Transform Selection to rotate 45° and scale for the desired amount of cut, and then use the result as a Layer Mask.
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If you use the Rectangle Tool to create a shape layer, then you can use this Corner Editor script
then Image>Trim.
https://photoshopscripts.wordpress.com/2015/07/29/corner-editor-update-for-photoshop-cc-2015/
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This is what clipping masks are used for. Use any shape you like -- super simple or complex custom shapes.
In this example, I used a puzzle piece from the Custom Shape library with a solid fill and border. Notice the Layers panel.