Yes there is another way to crop. Create a marquee with any of the tools available for doing so (marquee, pen to selection, select layer, etc...) then do Image -> Crop.
There's a bunch of ways to achieve what you're really looking for (based on comment). The first is by Cutting.
- Draw rounded rectangle
- Select just in from the curved corner
- Delete Button on keyboard. If it says you can't then you need to rasterize the layer. Right click on it on your layer palette and select rasterize.
You can also use the Pen Tool to for better results but doesn't really do any sort of deleting which is why I'm putting this second.
- Choose the vector rounded rectangle (No Rasterize)
- Choose the Convert Point Tool on your main toolbar, its in the Pen submenu
- Convert all the points on the side you want straight
- Choose the Delete Anchor Point Tool on the same menu
- Click on the two outer most points