How do i only cut this are and not the entire image?

[flint dew]

You can do that with the lasso tool or the polygonal lasso tool or any other in the selection toolset. Other types of selections include selection with subject based recognition (select> subject). You can also use the pen tool to create a path around what you need to cut and convert it into a selection. Once you have a selection, you can cut it (Press delete to cut it)
Better still, learn to use masks on a layer. When you paint on a mask, it hides the portion of the image you paint it on

More on selections:
https://helpx.adobe.com/uk/photoshop/using/making-selections.html
and Masks
https://www.youtube.com/watch?v=aNpO6G72O3w

[tired juniper]

Oh, thank you for the detailed reply.

[bright kestrel]

Gave +1 Creative Carma to @flint dew (current: #6 - 1155)