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How would I remove the selected object and the part of the other object taken up by it? enter image description here

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    $\begingroup$ Boolean operations are what you need youtube.com/watch?v=lDweCpDAB_o $\endgroup$ – Duarte Farrajota Ramos Apr 26 '16 at 17:44
  • $\begingroup$ Welcome to Blender Stack exchange, you might need to edit your question to explain better what you are willing to achieve. Remove the selected object might mean separate it to become an independent object, or might mean subtracting the selected mesh from the unselected. $\endgroup$ – Georges Apr 26 '16 at 17:57
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    $\begingroup$ Possible duplicate of Cut mesh at intersection $\endgroup$ – someonewithpc Apr 26 '16 at 18:22
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There are a few ways to do this.

Using Boolean operations:

  • In Edit mode

Both pieces have to be part of the same object.

On the selected piece use Mesh>Faces>Intersect(Boolean)

enter image description here

enter image description here

  • In Object Mode

Both pieces have to be different objects.

Select the one that is to be cut. And add a boolean modifier and use the other object to intersect.

enter image description here

This method has the advantage of being non destructive and interactive. If you need to reposition or alter the cutting object you can do it and the affected object will be recalculated.

At this point you can choose to hide other object or Apply the Modifier to make the change permanent and delete the cutting object.

enter image description here

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