You can make a selection in an image and then cut to that selection.
To cut a selection or layer:
Select the area or layer you want to cut. For information about making selections, see Making Selections in Images.
Choose Edit > Cut or press Ctrl + X.
Pasting a Cut or Copied Selection as a New Image
Pasting a Cut or Copied Selection as a New Layer
Pasting a Cut or Copied Selection into a Layer