Cut and Paste in same spot?

Basicly what I have is a picture on one layer. But I want to take a part of that picture, cut it, and put it on another layer. However, when I use the lasso tool or whatever to select it, I hit Ctrl+X to cut it and Ctrl+V to paste it. It pastes it on a new layer but it's in the center of the image. I want to cut it and paste it in the same spot that I selected it. Is this possible? Thank you.

Yes, it is possible. Select what you want to cut/paste. Then right click on the name of the layer you are cutting from and select 'Layer via Cut'